M. R. Evans and R. A. Blythe, Nonequilibrium dynamics in low-dimensional systems, Physica A: Statistical Mechanics and its Applications, vol.313, issue.1-2, p.110, 1991.
DOI : 10.1016/S0378-4371(02)01035-X

C. T. Macdonald, J. H. Gibbs, and A. C. Pipkin, Kinetics of biopolymerization on nucleic acid templates, Concerning the kinetics of polypeptide synthesis on polyribosomes, p.707, 1968.
DOI : 10.1002/bip.1968.360060102

T. Halpin-healy and Y. Zhang, Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics, Physics Reports, vol.254, issue.4-6, p.215, 1995.
DOI : 10.1016/0370-1573(94)00087-J

S. Klumpp and R. Lipowsky, Traffic of molecular motors through tube-like compartments, Journal of Statistical Physics, vol.113, issue.1/2, p.233, 2003.
DOI : 10.1023/A:1025778922620

B. Derrida, An exactly soluble non-equilibrium system: The asymmetric simple exclusion process, Physics Reports, vol.301, issue.1-3, p.65, 1998.
DOI : 10.1016/S0370-1573(98)00006-4

G. M. Schütz, Exactly Solvable Models for Many-Body Systems Far from Equilibrium, Equilibrium in Phase Transitions and Critical Phenomena vol, vol.19, 2001.
DOI : 10.1016/S1062-7901(01)80015-X

B. Schmittmann and R. K. Zia, Statistical mechanics of driven diffusive systems, Phase Transitions and Critical Phenomena, 1995.
DOI : 10.1016/S1062-7901(06)80014-5

S. Chatterjee and M. Barma, Shock probes in a one-dimensional Katz-Lebowitz-Spohn model arXiv, pp.707-1659, 2007.

T. Bodineau and B. Derrida, Current Fluctuations in Nonequilibrium Diffusive Systems: An Additivity Principle, Physical Review Letters, vol.92, issue.18, 2004.
DOI : 10.1103/PhysRevLett.92.180601

URL : https://hal.archives-ouvertes.fr/hal-00103472

J. L. Lebowitz and H. Spohn, 1999 A Gallavoti-Cohen type symmetry in the large deviation functional for stochastic dynamics, Journal of Statistical Physics, vol.95, issue.1/2, p.333
DOI : 10.1023/A:1004589714161

B. Derrida, M. R. Evans, V. Hakim, and V. Pasquier, Exact solution of a 1D asymmetric exclusion model using a matrix formulation, Journal of Physics A: Mathematical and General, vol.26, issue.7, 1493.
DOI : 10.1088/0305-4470/26/7/011

B. Derrida, S. A. Janowski, J. L. Lebowitz, and E. R. Speer, Exact solution of the totally asymmetric simple exclusion process: Shock profiles, Journal of Statistical Physics, vol.69, issue.5-6, p.813, 1993.
DOI : 10.1007/BF01052811

E. R. Speer, The two species totally asymmetric exclusion process, in Micro, Meso and Macroscopic approaches in Physics, M. Fannes C. Maes and A. Verbeure Ed. NATO Workshop 'On three levels, 1993.

K. Mallick, Shocks in the asymmetry exclusion model with an impurity, Journal of Physics A: Mathematical and General, vol.29, issue.17, p.5375, 1996.
DOI : 10.1088/0305-4470/29/17/013

C. Boutillier, P. François, K. Mallick, and S. Mallick, A matrix ansatz for the diffusion of an impurity in the asymmetric exclusion process, Journal of Physics A: Mathematical and General, vol.35, issue.46, p.9703, 2002.
DOI : 10.1088/0305-4470/35/46/301

K. Mallick, S. Mallick, and N. Rajewski, Exact solution of an exclusion process with three classes of particles and vacancies, Journal of Physics A: Mathematical and General, vol.32, issue.48, p.8399, 1999.
DOI : 10.1088/0305-4470/32/48/303

R. A. Blythe and M. R. Evans, Non-equilibrium steady states of matrix product form: a solver's guide, J, p.333, 2007.

D. Dhar, An exactly solved model for interfacial growth, Phase Transitions, vol.9, p.51, 1987.

L. Gwa and H. Spohn, Bethe solution for the dynamical-scaling exponent of the noisy Burgers equation, Physical Review A, vol.46, issue.2, 1992.
DOI : 10.1103/PhysRevA.46.844

D. Kim, chain and the Kardar-Parisi-Zhang-type growth model, Physical Review E, vol.52, issue.4, p.3512, 1995.
DOI : 10.1103/PhysRevE.52.3512

D. S. Lee and D. Kim, Large deviation function of the partially asymmetric exclusion process, Physical Review E, vol.59, issue.6, 1999.
DOI : 10.1103/PhysRevE.59.6476

O. Golinelli and K. Mallick, Spectral gap of the totally asymmetric exclusion process at arbitrary filling, Journal of Physics A: Mathematical and General, vol.38, issue.7, p.1419, 2005.
DOI : 10.1088/0305-4470/38/7/001

O. Golinelli and K. Mallick, Spectral Degeneracies in the Totally Asymmetric Exclusion Process, Journal of Statistical Physics, vol.88, issue.5-6, p.779, 2005.
DOI : 10.1007/s10955-005-6972-7

G. M. Schütz, A. Rákos, and G. M. Schütz, Exact solution of the master equation for the asymmetric exclusion process Bethe Ansatz and current distribution for the TASEP with particle-dependent hopping rates, J. Stat. Phys, vol.88, issue.427, p.506525, 1997.

B. Derrida and M. R. Evans, Bethe ansatz solution for a defect particle in the asymmetric exclusion process, Journal of Physics A: Mathematical and General, vol.32, issue.26, p.4833, 1999.
DOI : 10.1088/0305-4470/32/26/303

V. B. Priezzhev, Exact Nonstationary Probabilities in the Asymmetric Exclusion Process on a Ring, Physical Review Letters, vol.91, issue.5, p.50601, 2003.
DOI : 10.1103/PhysRevLett.91.050601

A. M. Povolotsky, Bethe ansatz solution of zero-range process with nonuniform stationary state, Physical Review E, vol.69, issue.6, 2004.
DOI : 10.1103/PhysRevE.69.061109

O. Golinelli and K. Mallick, The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics, Journal of Physics A: Mathematical and General, vol.39, issue.41, p.12679, 2006.
DOI : 10.1088/0305-4470/39/41/S03

B. Derrida and J. L. Lebowitz, Exact Large Deviation Function in the Asymmetric Exclusion Process, Physical Review Letters, vol.80, issue.2, p.209, 1998.
DOI : 10.1103/PhysRevLett.80.209

B. Derrida and C. Appert, Universal large-deviation function of the Kardar-Parisi-Zhang equation in one dimension, J. Stat. Phys, vol.94, issue.1, 1999.

B. Derrida, M. R. Evans, and D. , Exact diffusion constant for one-dimensional asymmetric exclusion models, Journal of Physics A: Mathematical and General, vol.26, issue.19, p.4911, 1993.
DOI : 10.1088/0305-4470/26/19/023

B. Derrida and K. Mallick, Exact diffusion constant for the one-dimensional partially asymmetric exclusion process, J. Phys. A: Math. Gen, vol.30, 1031.

C. Flindt, T. Novotn´ynovotn´y, A. Jauho, C. Flindt, T. Novotn´ynovotn´y et al., Current noise in a vibrating quantum dot array Full counting statistics of nano-electromechanical systems, Flindt et al., Counting Statistics of Non-Markovian Quantum Stochastic Processes, p.475, 2005.

E. Brunet and B. Derrida, Probability distribution of the free energy of a directed polymer in a random medium, Physical Review E, vol.61, issue.6, p.6789, 2000.
DOI : 10.1103/PhysRevE.61.6789

A. V. Razumov and Y. G. Stroganov, Bethe roots and refined enumeration of alternating-sign matrices, Journal of Statistical Mechanics: Theory and Experiment, vol.2006, issue.07, 2006.
DOI : 10.1088/1742-5468/2006/07/P07004

O. Babelon, A Short Introduction to classical and Quantum Integrable systems, Lecture Notes, 2007.

J. De-gier and F. H. Essler, Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries, Physical Review Letters, vol.95, issue.24, 2005.
DOI : 10.1103/PhysRevLett.95.240601

J. De-gier and F. H. Essler, Exact spectral gaps of the Asymmetric Exclusion Process with Open Boundaries, 2006.

T. M. Liggett, Interacting Particle Systems, 1985.

H. Spohn, Large Scale Dynamics of Interacting Particles, 1991.
DOI : 10.1007/978-3-642-84371-6

B. Derrida, An exactly soluble non-equilibrium system: The asymmetric simple exclusion process, Physics Reports, vol.301, issue.1-3, pp.65-83, 1998.
DOI : 10.1016/S0370-1573(98)00006-4

G. M. Schütz, Exactly Solvable Models for Many-Body Systems Far from Equilibrium, Phase Transitions and Critical Phenomena, 2001.
DOI : 10.1016/S1062-7901(01)80015-X

O. Golinelli and K. Mallick, The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics, Journal of Physics A: Mathematical and General, vol.39, issue.41, pp.12679-12705, 2006.
DOI : 10.1088/0305-4470/39/41/S03

D. Dhar, An exactly solved model for interfacial growth, Phase Transitions, vol.9, p.51, 1987.

L. Gwa and H. Spohn, Bethe solution for the dynamical-scaling exponent of the noisy Burgers equation, Physical Review A, vol.46, issue.2, pp.844-854, 1992.
DOI : 10.1103/PhysRevA.46.844

B. Derrida, M. R. Evans, V. Hakim, and V. Pasquier, Exact solution of a 1D asymmetric exclusion model using a matrix formulation, Journal of Physics A: Mathematical and General, vol.26, issue.7, pp.1493-1517, 1993.
DOI : 10.1088/0305-4470/26/7/011

R. A. Blythe and M. Evans, Nonequilibrium steady states of matrix-product form: a solver's guide, Journal of Physics A: Mathematical and Theoretical, vol.40, issue.46, pp.333-441, 2007.
DOI : 10.1088/1751-8113/40/46/R01

B. Derrida and J. L. Lebowitz, Exact Large Deviation Function in the Asymmetric Exclusion Process, Physical Review Letters, vol.80, issue.2, pp.209-213, 1998.
DOI : 10.1103/PhysRevLett.80.209

B. Derrida and M. R. Evans, Bethe ansatz solution for a defect particle in the asymmetric exclusion process, Journal of Physics A: Mathematical and General, vol.32, issue.26, pp.4833-4850, 1999.
DOI : 10.1088/0305-4470/32/26/303

T. Bodineau and B. Derrida, Distribution of current in non-equilibrium diffusive systems and phase transitions, Phys. Rev. E, issue.6, p.72066110, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00018380

C. Boutillier, P. François, K. Mallick, and S. Mallick, A matrix ansatz for the diffusion of an impurity in the asymmetric exclusion process, Journal of Physics A: Mathematical and General, vol.35, issue.46, pp.9703-9730, 2002.
DOI : 10.1088/0305-4470/35/46/301

M. Prähofer and H. Spohn, Current fluctuations for the totally asymmetric simple exclusion process In In and Out of Equilibrium: Probability with a Physics Flavor, Progress in Probability, vol.51, pp.185-204, 2002.

T. Sasamoto, Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques, Journal of Statistical Mechanics: Theory and Experiment, vol.2007, issue.07, p.7007, 2007.
DOI : 10.1088/1742-5468/2007/07/P07007

D. S. Lee and D. Kim, Large deviation function of the partially asymmetric exclusion process, Physical Review E, vol.59, issue.6, pp.6476-6482, 1999.
DOI : 10.1103/PhysRevE.59.6476

B. Derrida and K. Mallick, Exact diffusion constant for the one-dimensional partially asymmetric exclusion model, Journal of Physics A: Mathematical and General, vol.30, issue.4, pp.1031-1046, 1997.
DOI : 10.1088/0305-4470/30/4/007

S. Prolhac and K. Mallick, Current fluctuations in the exclusion process and Bethe ansatz, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.17, p.41175002, 2008.
DOI : 10.1088/1751-8113/41/17/175002

URL : https://hal.archives-ouvertes.fr/hal-00796141

J. L. Lebowitz and H. Spohn, A Gallavoti-Cohen type symmetry in the large deviation functional for stochastic dynamics, Journal of Statistical Physics, vol.95, issue.1/2, pp.333-365, 1999.
DOI : 10.1023/A:1004589714161

R. J. Baxter, Exactly Solved Models in Statistical Mechanics, 1982.
DOI : 10.1142/9789814415255_0002

Y. G. Stroganov, The importance of being odd, Journal of Physics A: Mathematical and General, vol.34, issue.13, pp.179-185, 2001.
DOI : 10.1088/0305-4470/34/13/104

R. I. Nepomechie, Functional relations and Bethe Ansatz for the XXZ chain, Journal of Statistical Physics, vol.111, issue.5/6, pp.1363-1376, 2003.
DOI : 10.1023/A:1023016602955

P. Dorey, C. Dunning, and R. Tateo, The ODE/IM correspondence, Journal of Physics A: Mathematical and Theoretical, vol.40, issue.32, pp.205-283, 2007.
DOI : 10.1088/1751-8113/40/32/R01

C. Appert, B. Derrida, V. Lecomte, and F. Van-wijland, Universal cumulants of the current in diffusive systems on a ring, p.2590, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00273794

J. De-gier and F. H. Essler, Exact spectral gaps of the asymmetric exclusion process with open boundaries, Phys. Rev. Lett, issue.24, p.95240601, 2005.

W. Galleas, Functional relations from the Yang???Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions, Nuclear Physics B, vol.790, issue.3, pp.524-542, 2008.
DOI : 10.1016/j.nuclphysb.2007.09.011

B. Derrida and C. Appert, Universal large-deviation function of the Kardar-Parisi-Zhang equation in one dimension, Journal of Statistical Physics, vol.94, issue.1/2, pp.1-30, 1999.
DOI : 10.1023/A:1004519626804

B. Reulet, Higher moments of noise In proceedings of Les Houches Summer School session LXXXI, 2005.

P. Paule and M. Schorn, A Mathematica Version of Zeilberger's Algorithm for Proving Binomial Coefficient Identities, Journal of Symbolic Computation, vol.20, issue.5-6, pp.673-698, 1995.
DOI : 10.1006/jsco.1995.1071

F. Spitzer, Interaction of Markov processes, Advances in Mathematics, vol.5, issue.2, pp.246-290, 1970.
DOI : 10.1016/0001-8708(70)90034-4

T. M. Liggett, Interacting Particle Systems, 1985.

P. A. Ferrari, Exclusion processes and applications (lecture notes of a course given at Institut Henri Poincarré), 2008.

S. Katz, J. L. Lebowitz, and H. Spohn, Nonequilibrium steady states of stochastic lattice gas models of fast ionic conductors, Journal of Statistical Physics, vol.141, issue.3-4, pp.497-537, 1984.
DOI : 10.1007/BF01018556

H. Spohn, Large Scale Dynamics of Interacting Particles, 1991.
DOI : 10.1007/978-3-642-84371-6

T. Halpin-healy and Y. Zhang, Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics, Physics Reports, vol.254, issue.4-6, pp.215-414, 1995.
DOI : 10.1016/0370-1573(94)00087-J

B. Schmittmann and R. K. Zia, Statistical mechanics of driven diffusive systems, Phase Transitions and Critical Phenomena, 1995.
DOI : 10.1016/S1062-7901(06)80014-5

B. Derrida, An exactly soluble non-equilibrium system: The asymmetric simple exclusion process, Physics Reports, vol.301, issue.1-3, pp.65-83, 1998.
DOI : 10.1016/S0370-1573(98)00006-4

G. M. Schütz, Exactly Solvable Models for Many-Body Systems Far from Equilibrium, Phase Transitions and Critical Phenomena, 2001.
DOI : 10.1016/S1062-7901(01)80015-X

O. Golinelli and K. Mallick, The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics, Journal of Physics A: Mathematical and General, vol.39, issue.41, pp.12679-12705, 2006.
DOI : 10.1088/0305-4470/39/41/S03

B. Derrida, Non-equilibrium steady states: fluctuations and large deviations of the density and of the current, Journal of Statistical Mechanics: Theory and Experiment, vol.2007, issue.07, p.7023, 2007.
DOI : 10.1088/1742-5468/2007/07/P07023

S. F. Edwards and D. R. Wilkinson, The Surface Statistics of a Granular Aggregate, Proc. R. Soc. A, pp.17-31, 1982.
DOI : 10.1098/rspa.1982.0056

M. Kardar, G. Parisi, and Y. Zhang, Dynamic Scaling of Growing Interfaces, Physical Review Letters, vol.56, issue.9, pp.889-892, 1986.
DOI : 10.1103/PhysRevLett.56.889

M. Evans and T. Hanney, Nonequilibrium statistical mechanics of the zero-range process and related models, Journal of Physics A: Mathematical and General, vol.38, issue.19, pp.195-240, 2005.
DOI : 10.1088/0305-4470/38/19/R01

J. Krug, Origins of scale invariance in growth processes, Advances in Physics, vol.16, issue.2, pp.139-282, 1997.
DOI : 10.1209/0295-5075/32/2/011

L. Gwa and H. Spohn, Six-vertex model, roughened surfaces, and an asymmetric spin Hamiltonian, Physical Review Letters, vol.68, issue.6, pp.725-728, 1992.
DOI : 10.1103/PhysRevLett.68.725

D. Kandel, E. Domany, and B. Nienhuis, A six-vertex model as a diffusion problem: derivation of correlation functions, Journal of Physics A: Mathematical and General, vol.23, issue.15, pp.755-762, 1990.
DOI : 10.1088/0305-4470/23/15/011

F. H. Essler and V. Rittenberg, Representations of the quadratic algebra and partially asymmetric diffusion with open boundaries, Journal of Physics A: Mathematical and General, vol.29, issue.13, pp.3375-3407, 1996.
DOI : 10.1088/0305-4470/29/13/013

R. Lipowsky, S. Klumpp, and T. M. Nieuwenhuizen, Random Walks of Cytoskeletal Motors in Open and Closed Compartments, Physical Review Letters, vol.87, issue.10, p.108101, 2001.
DOI : 10.1103/PhysRevLett.87.108101

P. M. Richards, Theory of one-dimensional hopping conductivity and diffusion, Physical Review B, vol.16, issue.4, pp.1393-1409, 1977.
DOI : 10.1103/PhysRevB.16.1393

D. Chowdhury, L. Santen, and A. Schadschneider, Statistical physics of vehicular traffic and some related systems, Physics Reports, vol.329, issue.4-6, pp.199-329, 2000.
DOI : 10.1016/S0370-1573(99)00117-9

B. Derrida, M. R. Evans, V. Hakim, and V. Pasquier, Exact solution of a 1D asymmetric exclusion model using a matrix formulation, Journal of Physics A: Mathematical and General, vol.26, issue.7, pp.1493-1517, 1993.
DOI : 10.1088/0305-4470/26/7/011

R. A. Blythe and M. Evans, Nonequilibrium steady states of matrix-product form: a solver's guide, Journal of Physics A: Mathematical and Theoretical, vol.40, issue.46, pp.333-441, 2007.
DOI : 10.1088/1751-8113/40/46/R01

M. Prähofer and H. Spohn, Current fluctuations for the totally asymmetric simple exclusion process In In and Out of Equilibrium: Probability with a Physics Flavor, Progress in Probability, vol.51, pp.185-204, 2002.

H. Spohn, Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals, Physica A: Statistical Mechanics and its Applications, vol.369, issue.1, pp.71-99, 2006.
DOI : 10.1016/j.physa.2006.04.006

T. Sasamoto, Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques, Journal of Statistical Mechanics: Theory and Experiment, vol.2007, issue.07, p.7007, 2007.
DOI : 10.1088/1742-5468/2007/07/P07007

D. Dhar, An exactly solved model for interfacial growth, Phase Transitions, vol.9, p.51, 1987.

J. De-gier and F. H. Essler, Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries, Physical Review Letters, vol.95, issue.24, p.240601, 2005.
DOI : 10.1103/PhysRevLett.95.240601

J. De-gier and F. H. Essler, Exact spectral gaps of the asymmetric exclusion process with open boundaries, J. Stat. Mech, p.12011, 2006.

D. Kim, chain and the Kardar-Parisi-Zhang-type growth model, Physical Review E, vol.52, issue.4, pp.3512-3524, 1995.
DOI : 10.1103/PhysRevE.52.3512

O. Golinelli and K. Mallick, Bethe ansatz calculation of the spectral gap of the asymmetric exclusion process, Journal of Physics A: Mathematical and General, vol.37, issue.10, pp.3321-3331, 2004.
DOI : 10.1088/0305-4470/37/10/001

O. Golinelli and K. Mallick, Spectral gap of the totally asymmetric exclusion process at arbitrary filling, Journal of Physics A: Mathematical and General, vol.38, issue.7, pp.1419-1425, 2005.
DOI : 10.1088/0305-4470/38/7/001

J. De-gier and F. H. Essler, Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.48, p.485002, 2008.
DOI : 10.1088/1751-8113/41/48/485002

B. Derrida and J. L. Lebowitz, Exact Large Deviation Function in the Asymmetric Exclusion Process, Physical Review Letters, vol.80, issue.2, pp.209-213, 1998.
DOI : 10.1103/PhysRevLett.80.209

B. Derrida and C. Appert, Universal large-deviation function of the Kardar-Parisi-Zhang equation in one dimension, Journal of Statistical Physics, vol.94, issue.1/2, pp.1-30, 1999.
DOI : 10.1023/A:1004519626804

D. S. Lee and D. Kim, Large deviation function of the partially asymmetric exclusion process, Physical Review E, vol.59, issue.6, pp.6476-6482, 1999.
DOI : 10.1103/PhysRevE.59.6476

B. Derrida and M. R. Evans, Bethe ansatz solution for a defect particle in the asymmetric exclusion process, Journal of Physics A: Mathematical and General, vol.32, issue.26, pp.4833-4850, 1999.
DOI : 10.1088/0305-4470/32/26/303

C. Appert-rolland, B. Derrida, V. Lecomte, and F. Van-wijland, Universal cumulants of the current in diffusive systems on a ring, Physical Review E, vol.78, issue.2, p.21122, 2008.
DOI : 10.1103/PhysRevE.78.021122

URL : https://hal.archives-ouvertes.fr/hal-00273794

S. Prolhac and K. Mallick, Current fluctuations in the exclusion process and Bethe ansatz, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.17, p.175002, 2008.
DOI : 10.1088/1751-8113/41/17/175002

URL : https://hal.archives-ouvertes.fr/hal-00796141

S. Prolhac, Fluctuations and skewness of the current in the partially asymmetric exclusion process, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.36, p.365003, 2008.
DOI : 10.1088/1751-8113/41/36/365003

URL : https://hal.archives-ouvertes.fr/hal-00796151

L. Bertini, A. De-sole, D. Gabrielli, G. Jona-lasinio, and C. Landim, Fluctuations in Stationary Nonequilibrium States of Irreversible Processes, Physical Review Letters, vol.87, issue.4, p.40601, 2001.
DOI : 10.1103/PhysRevLett.87.040601

L. Bertini, A. De-sole, D. Gabrielli, G. Jona-lasinio, and C. Landim, Macroscopic fluctuation theory for stationary non-equilibrium states, Journal of Statistical Physics, vol.107, issue.3/4, pp.635-675, 2004.
DOI : 10.1023/A:1014525911391

J. L. Lebowitz and H. Spohn, A Gallavotti-Cohen-type symmetry in the large deviation functional for stochastic dynamics, Journal of Statistical Physics, vol.95, issue.1/2, pp.333-365, 1999.
DOI : 10.1023/A:1004589714161

B. Derrida and K. Mallick, Exact diffusion constant for the one-dimensional partially asymmetric exclusion model, Journal of Physics A: Mathematical and General, vol.30, issue.4, pp.1031-1046, 1997.
DOI : 10.1088/0305-4470/30/4/007

T. Bodineau and B. Derrida, Distribution of current in nonequilibrium diffusive systems and phase transitions, Physical Review E, vol.72, issue.6, p.66110, 2005.
DOI : 10.1103/PhysRevE.72.066110

URL : https://hal.archives-ouvertes.fr/hal-00018380

F. C. Alcaraz and R. Z. Bariev, Exact solution of asymmetric diffusion with N classes of particles of arbitrary size and hierarchical order, Brazilian Journal of Physics, vol.30, issue.4, pp.655-666, 2000.
DOI : 10.1590/S0103-97332000000400004

O. Babelon, A short introduction to classical and quantum integrable systems (lecture notes of a course given at IPhT, CEA Saclay), 2007.

O. Golinelli and K. Mallick, Family of commuting operators for the totally asymmetric exclusion process, Journal of Physics A: Mathematical and Theoretical, vol.40, issue.22, pp.5795-5812, 2007.
DOI : 10.1088/1751-8113/40/22/003

O. Golinelli and K. Mallick, Connected operators for the totally asymmetric exclusion process, Journal of Physics A: Mathematical and Theoretical, vol.40, issue.44, pp.13231-13236, 2007.
DOI : 10.1088/1751-8113/40/44/004

H. Spohn, Large Scale Dynamics of Interacting Particles, 1991.
DOI : 10.1007/978-3-642-84371-6

T. Halpin-healy and Y. Zhang, Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics, Physics Reports, vol.254, issue.4-6, pp.215-414, 1995.
DOI : 10.1016/0370-1573(94)00087-J

B. Schmittmann and R. K. Zia, Driven diffusive systems. An introduction and recent developments, Physics Reports, vol.301, issue.1-3, pp.45-64, 1998.
DOI : 10.1016/S0370-1573(98)00005-2

B. Derrida, Non-equilibrium steady states: fluctuations and large deviations of the density and of the current, Journal of Statistical Mechanics: Theory and Experiment, vol.2007, issue.07, p.7023, 2007.
DOI : 10.1088/1742-5468/2007/07/P07023

B. Derrida, J. L. Lebowitz, and E. Speer, Exact Free Energy Functional for a Driven Diffusive Open Stationary Nonequilibrium System, Physical Review Letters, vol.89, issue.3, p.30601, 2002.
DOI : 10.1103/PhysRevLett.89.030601

J. De-gier and F. H. Essler, Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries, Physical Review Letters, vol.95, issue.24, p.240601, 2005.
DOI : 10.1103/PhysRevLett.95.240601

H. Spohn, Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals, Physica A: Statistical Mechanics and its Applications, vol.369, issue.1, pp.71-99, 2006.
DOI : 10.1016/j.physa.2006.04.006

T. Sasamoto, Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques, Journal of Statistical Mechanics: Theory and Experiment, vol.2007, issue.07, p.7007, 2007.
DOI : 10.1088/1742-5468/2007/07/P07007

A. Rákos and G. M. Schütz, Bethe ansatz and current distribution for the TASEP with particle-dependent hopping rates. Markov Processes and Related Fields, pp.323-334, 2006.

O. Golinelli and K. Mallick, The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics, Journal of Physics A: Mathematical and General, vol.39, issue.41, pp.12679-12705, 2006.
DOI : 10.1088/0305-4470/39/41/S03

B. Derrida and M. R. Evans, Bethe ansatz solution for a defect particle in the asymmetric exclusion process, Journal of Physics A: Mathematical and General, vol.32, issue.26, pp.4833-4850, 1999.
DOI : 10.1088/0305-4470/32/26/303

V. B. Priezzhev, Exact Nonstationary Probabilities in the Asymmetric Exclusion Process on a Ring, Physical Review Letters, vol.91, issue.5, p.50601, 2003.
DOI : 10.1103/PhysRevLett.91.050601

B. Derrida and J. L. Lebowitz, Exact Large Deviation Function in the Asymmetric Exclusion Process, Physical Review Letters, vol.80, issue.2, pp.209-213, 1998.
DOI : 10.1103/PhysRevLett.80.209

S. Prolhac and K. Mallick, Current fluctuations in the exclusion process and Bethe ansatz, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.17, p.175002, 2008.
DOI : 10.1088/1751-8113/41/17/175002

URL : https://hal.archives-ouvertes.fr/hal-00796141

S. Prolhac, Fluctuations and skewness of the current in the partially asymmetric exclusion process, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.36, p.365003, 2008.
DOI : 10.1088/1751-8113/41/36/365003

URL : https://hal.archives-ouvertes.fr/hal-00796151

D. S. Lee and D. Kim, Large deviation function of the partially asymmetric exclusion process, Physical Review E, vol.59, issue.6, pp.6476-6482, 1999.
DOI : 10.1103/PhysRevE.59.6476

R. J. Baxter, Exactly Solved Models in Statistical Mechanics, 1982.
DOI : 10.1142/9789814415255_0002

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009.
DOI : 10.1017/CBO9780511801655

URL : https://hal.archives-ouvertes.fr/inria-00072739

S. Prolhac and K. Mallick, Cumulants of the current in a weakly asymmetric exclusion process, Journal of Physics A: Mathematical and Theoretical, vol.42, issue.17, p.175001, 2009.
DOI : 10.1088/1751-8113/42/17/175001

H. A. Spohn-]-r, M. R. Blythe, and . Evans, Large scale dynamics of interacting particles Nonequilibrium steady states of matrix-product form: a solver's guide, J. Phys. A: Math. Theor, vol.40, issue.3, p.333, 1991.

B. Derrida, An exactly soluble non-equilibrium system: The asymmetric simple exclusion process, Physics Reports, vol.301, issue.1-3, pp.65-83, 1998.
DOI : 10.1016/S0370-1573(98)00006-4

O. Golinelli and K. Mallick, The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics, Journal of Physics A: Mathematical and General, vol.39, issue.41, pp.12679-12705, 2006.
DOI : 10.1088/0305-4470/39/41/S03

B. Derrida, M. R. Evans, and D. Mukamel, Exact diffusion constant for the one-dimensional asymmetric exclusion models, J. Phys. A, vol.36, pp.4911-4918, 1993.

B. Derrida and K. Mallick, Exact diffusion constant for the one-dimensional partially asymmetric exclusion model, Journal of Physics A: Mathematical and General, vol.30, issue.4, pp.1031-1046, 1997.
DOI : 10.1088/0305-4470/30/4/007

S. Prolhac and K. Mallick, Current fluctuations in the exclusion process and Bethe ansatz, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.17, p.175002, 2008.
DOI : 10.1088/1751-8113/41/17/175002

URL : https://hal.archives-ouvertes.fr/hal-00796141

B. Derrida and J. L. Lebowitz, Exact Large Deviation Function in the Asymmetric Exclusion Process, Physical Review Letters, vol.80, issue.2, pp.209-213, 1998.
DOI : 10.1103/PhysRevLett.80.209

B. Derrida, M. R. Evans, V. Hakim, and V. Pasquier, Exact solution of a 1D asymmetric exclusion model using a matrix formulation, Journal of Physics A: Mathematical and General, vol.26, issue.7, pp.1493-1517, 1993.
DOI : 10.1088/0305-4470/26/7/011

F. H. Essler and V. Rittenberg, Representations of the quadratic algebra and partially asymmetric diffusion with open boundaries, Journal of Physics A: Mathematical and General, vol.29, issue.13, pp.3375-3407, 1996.
DOI : 10.1088/0305-4470/29/13/013

T. Sasamoto, One-dimensional partially asymmetric simple exclusion process with open boundaries: orthogonal polynomials approach, Journal of Physics A: Mathematical and General, vol.32, issue.41, pp.7109-7131, 1999.
DOI : 10.1088/0305-4470/32/41/306

R. A. Blythe, M. R. Evans, F. Colaiori, and F. H. , Exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra, Journal of Physics A: Mathematical and General, vol.33, issue.12, pp.2313-2332, 2000.
DOI : 10.1088/0305-4470/33/12/301

M. R. Evans and R. A. Blythe, Nonequilibrium dynamics in low-dimensional systems, Physica A: Statistical Mechanics and its Applications, vol.313, issue.1-2, p.110, 2002.
DOI : 10.1016/S0378-4371(02)01035-X

K. Mallick and S. Sandow, Finite-dimensional representations of the quadratic algebra: Applications to the exclusion process, Journal of Physics A: Mathematical and General, vol.30, issue.13, pp.4513-4526, 1997.
DOI : 10.1088/0305-4470/30/13/008

C. Boldrighini, G. Cosimi, S. Frigio, and M. G. Nunes, Computer simulation of shock waves in the completely asymmetric simple exclusion process, Journal of Statistical Physics, vol.18, issue.3-4, p.611, 1989.
DOI : 10.1007/BF01041600

P. A. Ferrari, C. Kipnis, and E. Saada, Microscopic Structure of Travelling Waves in the Asymmetric Simple Exclusion Process, The Annals of Probability, vol.19, issue.1, pp.226-244, 1991.
DOI : 10.1214/aop/1176990542

P. A. Ferrari, Microscopic shocks in one dimensional driven system, Ann. Inst. Henri Poinc, vol.55, p.637, 1991.

B. Derrida, S. A. Janowsky, J. L. Lebowitz, and E. R. Speer, Exact solution of the totally asymmetric simple exclusion process: Shock profiles, Journal of Statistical Physics, vol.69, issue.5-6, p.8312, 1993.
DOI : 10.1007/BF01052811

K. Mallick, Shocks in the asymmetry exclusion model with an impurity, Journal of Physics A: Mathematical and General, vol.29, issue.17, pp.5375-5386, 1996.
DOI : 10.1088/0305-4470/29/17/013

V. Karimipour, Multispecies asymmetric simple exclusion process and its relation to traffic flow, Physical Review E, vol.59, issue.1, pp.205-212, 1999.
DOI : 10.1103/PhysRevE.59.205

M. Khorrami and V. Karimipour, Exact determination of the phase structure of a multi-species asymmetric exclusion process, Journal of Statistical Physics, vol.100, issue.5/6, pp.999-1030, 2000.
DOI : 10.1023/A:1018758907902

P. F. Arndt, T. Heinzel, and V. Rittenberg, Spontaneous breaking of translational invariance in one-dimensional stationary states on a ring, Journal of Physics A: Mathematical and General, vol.31, issue.2, pp.31-45, 1998.
DOI : 10.1088/0305-4470/31/2/001

A. P. Isaev and P. N. , Diffusion algebras, Journal of Physics A: Mathematical and General, vol.34, issue.29, pp.5815-5834, 2001.
DOI : 10.1088/0305-4470/34/29/306

K. Mallick, S. Mallick, and N. Rajewsky, Exact solution of an exclusion process with three classes of particles and vacancies, Journal of Physics A: Mathematical and General, vol.32, issue.48, pp.8399-8410, 1999.
DOI : 10.1088/0305-4470/32/48/303

P. A. Ferrari and J. B. , Stationary distributions of multi-type totally asymmetric exclusion processes, The Annals of Probability, vol.35, issue.3, p.807, 2007.
DOI : 10.1214/009117906000000944

M. R. Evans, P. A. Ferrari, and K. Mallick, Matrix Representation of the Stationary Measure for??the??Multispecies TASEP, Journal of Statistical Physics, vol.33, issue.2, pp.10955-10964, 2008.
DOI : 10.1007/s10955-009-9696-2

O. Angel, The stationary measure of a 2-type totally asymmetric exclusion process, Journal of Combinatorial Theory, Series A, vol.113, issue.4, p.625, 2006.
DOI : 10.1016/j.jcta.2005.05.004

H. Hinrichsen and S. , On matrix product ground states for reaction - diffusion models, Journal of Physics A: Mathematical and General, vol.29, issue.11, p.2643, 1996.
DOI : 10.1088/0305-4470/29/11/005

N. Rajewsky, L. Santen, A. Schadschneider, and M. Schreckenberg, The asymmetric exclusion process: Comparison of update procedures, Journal of Statistical Physics, vol.92, issue.1/2, pp.151-194, 1998.
DOI : 10.1023/A:1023047703307

M. R. Evans, Y. Kafri, H. M. Koduvely, and D. Mukamel, Phase Separation in One-Dimensional Driven Diffusive Systems, Physical Review Letters, vol.80, issue.3, p.425, 1998.
DOI : 10.1103/PhysRevLett.80.425

D. Dhar, An exactly solved model for interfacial growth, Phase Transitions, vol.9, p.51, 1987.

L. Gwa and H. Spohn, Bethe solution for the dynamical-scaling exponent of the noisy Burgers equation, Physical Review A, vol.46, issue.2, p.844, 1992.
DOI : 10.1103/PhysRevA.46.844

O. Golinelli and K. Mallick, Spectral gap of the totally asymmetric exclusion process at arbitrary filling, Journal of Physics A: Mathematical and General, vol.38, issue.7, pp.1419-1425, 2005.
DOI : 10.1088/0305-4470/38/7/001

J. De-gier and F. H. Essler, Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries, J. Stat. Mech, p.12011, 2006.

B. Derrida and M. R. Evans, Bethe ansatz solution for a defect particle in the asymmetric exclusion process, Journal of Physics A: Mathematical and General, vol.32, issue.26, p.4833, 1999.
DOI : 10.1088/0305-4470/32/26/303

F. C. Alcaraz and R. Z. Bariev, Exact solution of asymmetric diffusion with second-class particles of arbitrary size, Brazilian Journal of Physics, vol.30, issue.1, p.13, 2000.
DOI : 10.1590/S0103-97332000000100003

L. Cantini, Algebraic Bethe ansatz for the two species ASEP with different hopping rates, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.9, pp.41-095001, 2008.
DOI : 10.1088/1751-8113/41/9/095001