H. Rousset, On a probabilistic interpretation of shape derivatives of Dirichlet groundstates with application to Fermion nodes, ESAIM: Mathematical Modelling and Numerical Analysis, vol.44, issue.5, 2010.
DOI : 10.1051/m2an/2010049

URL : https://hal.archives-ouvertes.fr/inria-00447396

T. Goudon and M. Rousset, Stochastic Acceleration in an Inhomogeneous Time Random Force Field, H7] ( * ) P. Plechac and M. Rousset, Implicit Mass-Matrix Penalization of Hamiltonian dynamics with application to exact sampling of stiff systems, pp.1-46, 2009.
DOI : 10.1093/amrx/abp001

T. Lelì-evre, M. Rousset, and G. Stoltz, Long-time convergence of an adaptive biasing force method, Nonlinearity, vol.21, issue.6, pp.1155-1181, 2008.
DOI : 10.1088/0951-7715/21/6/001

T. Lelì-evre, M. Rousset, and G. Stoltz, Computation of free energy profiles with parallel adaptive dynamics, J. Chem. Phys, vol.126, p.13, 2007.

P. , T. Lelì-evre, M. Rousset, and G. Stoltz, Computation of free energy differences through non-equilibrium stochastic dynamics: the reaction coordinate case, Publications from works completed or initiated before or during my PhD, pp.624-643, 2007.

M. Rousset and G. Stoltz, Equilibrium Sampling From Nonequilibrium Dynamics, Journal of Statistical Physics, vol.22, issue.3, pp.1251-1272, 2006.
DOI : 10.1007/s10955-006-9090-2

URL : http://arxiv.org/abs/cond-mat/0511412

M. Rousset, On the Control of an Interacting Particle Estimation of Schr??dinger Ground States, SIAM Journal on Mathematical Analysis, vol.38, issue.3, pp.824-844, 2006.
DOI : 10.1137/050640667

M. Rousset, Sur la rigidit?? de poly??dres hyperboliques en dimension $3$ : cas de volume fini, cas hyperid??al, cas fuchsien, Bulletin de la Société mathématique de France, vol.132, issue.2, pp.233-261, 2004.
DOI : 10.24033/bsmf.2465

URL : http://arxiv.org/abs/math/0211280

C. Asymptotically-stable, Application: asymptotic variance reduction of simulations, p.44

W. Alt, Orientation of cells migrating in a chemotactic gradient, Adv Appl Probab, vol.12, issue.3, pp.566-566, 1980.

L. Ambrosio, N. Gigli, and G. Savaré, Gradient flows: in metric spaces and in the space of probability measures, 2006.

R. Assaraf and M. Caffarel, A pedagogical introduction to Quantum Monte Carlo, 2000.

R. Assaraf and M. Caffarel, Zero-variance zero-bias principle for observables in quantum Monte Carlo: Application to forces, The Journal of Chemical Physics, vol.119, issue.20, pp.10536-10552, 2003.
DOI : 10.1063/1.1621615

URL : https://hal.archives-ouvertes.fr/hal-00000683

R. Assaraf, M. Caffarel, and A. Khelif, Diffusion Monte Carlo methods with a fixed number of walkers, Physical Review E, vol.61, issue.4, pp.4566-4575, 2000.
DOI : 10.1103/PhysRevE.61.4566

A. Badinski, P. D. Haynes, and R. J. Needs, Nodal Pulay terms for accurate diffusion quantum Monte Carlo forces, Physical Review B, vol.77, issue.8, p.85111, 2008.
DOI : 10.1103/PhysRevB.77.085111

A. Badinski and R. J. Needs, Total forces in the diffusion Monte Carlo method with nonlocal pseudopotentials, Physical Review B, vol.78, issue.3, p.35134, 2008.
DOI : 10.1103/PhysRevB.78.035134

D. Bakry, I. Gentil, and M. Ledoux, Analysis and geometry of Markov diffusion operators, 2014.
DOI : 10.1007/978-3-319-00227-9

URL : https://hal.archives-ouvertes.fr/hal-00929960

C. H. Bennett, Mass tensor molecular dynamics, Journal of Computational Physics, vol.19, issue.3, pp.267-279, 1975.
DOI : 10.1016/0021-9991(75)90077-7

A. Bobylev, The theory of the nonlinear boltzmann equation for maxwell molecules, Mathematical physics reviews, vol.7, issue.111, 1988.

A. Bobylev and C. Cercignani, On the rate of entropy production for the boltzmann equation, Journal of Statistical Physics, vol.94, issue.3/4, pp.603-618, 1999.
DOI : 10.1023/A:1004537522686

F. Bolley, I. Gentil, and A. Guillin, Convergence to equilibrium in Wasserstein distance for Fokker???Planck equations, Journal of Functional Analysis, vol.263, issue.8, 2012.
DOI : 10.1016/j.jfa.2012.07.007

URL : https://hal.archives-ouvertes.fr/hal-00632941

F. Bolley, I. Gentil, and A. Guillin, Uniform convergence to equilibrium for granular media, Archive for Rational Mechanics and Analysis, pp.1-17, 2012.

F. Bornemann and C. Schütte, Homogenization of Hamiltonian systems with a strong constraining potential, Physica D: Nonlinear Phenomena, vol.102, issue.1-2, pp.57-77, 1992.
DOI : 10.1016/S0167-2789(96)00245-X

N. Bournaveas and V. Calvez, Global existence for the kinetic chemotaxis model without pointwise memory effects, and including internal variables, Kinet. Relat. Models, vol.1, issue.1, pp.29-48, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00256288

A. Bren and M. Eisenbach, How Signals Are Heard during Bacterial Chemotaxis: Protein-Protein Interactions in Sensory Signal Propagation, Journal of Bacteriology, vol.182, issue.24, pp.6865-6873, 2000.
DOI : 10.1128/JB.182.24.6865-6873.2000

E. Cancès, B. Jourdain, and T. Lelì-evre, Quantum monte-carlo simulations of fermions. a mathematical analysis of the fixed-node approximation, Math. Mod. and Meth. in App. Sci, pp.16-1403, 2006.

E. Carlen and M. Carvalho, Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation, Journal of Statistical Physics, vol.47, issue.3-4, pp.3-4, 1992.
DOI : 10.1007/BF01049721

A. Eric, . Carlen, C. Maria, M. Carvalho, and . Loss, Determination of the spectral gap for kac´skac´s master equation and related stochastic evolution, Acta mathematica, vol.191, issue.1, pp.1-54, 2003.

A. Eric, . Carlen, S. Jeffrey, M. Geronimo, and . Loss, Determination of the spectral gap in the kac's model for physical momentum and energy-conserving collisions, SIAM Journal on Mathematical Analysis, vol.40, issue.1, pp.327-364, 2008.

A. Eric, X. Carlen, and . Lu, Fast and slow convergence to equilibrium for maxwellian molecules via wild sums, Journal of statistical physics, vol.112, issue.12, pp.59-134, 2003.

M. Casalegno, M. Mella, and A. M. Rappe, Computing accurate forces in quantum Monte Carlo using Pulay???s corrections and energy minimization, The Journal of Chemical Physics, vol.118, issue.16, pp.7193-7201, 2003.
DOI : 10.1063/1.1562605

URL : http://hdl.handle.net/11383/1735827

D. Ceperley, G. V. Chester, and M. H. Kalos, Monte Carlo simulation of a many-fermion study, Physical Review B, vol.16, issue.7, pp.3081-3099, 1977.
DOI : 10.1103/PhysRevB.16.3081

D. M. Ceperley, Fermion nodes, Journal of Statistical Physics, vol.45, issue.5-6, pp.1237-1267, 1991.
DOI : 10.1007/BF01030009

D. M. Ceperley and B. J. Alder, Ground State of the Electron Gas by a Stochastic Method, Physical Review Letters, vol.45, issue.7, pp.566-569, 1980.
DOI : 10.1103/PhysRevLett.45.566

C. Cercignani, Mathematical methods in kinetic theory, 1969.

C. Cercignani, H-theorem and trend to equilibrium in the kinetic theory of gases, Archiv of Mechanics, Archiwum Mechaniki Stosowanej, vol.34, pp.231-241, 1982.

F. Chalub, P. Markowich, C. Perthame, and . Schmeiser, Kinetic Models for Chemotaxis and their Drift-Diffusion Limits, Monatshefte f???r Mathematik, vol.142, issue.1-2, pp.123-141, 2004.
DOI : 10.1007/s00605-004-0234-7

P. , D. Moral, and F. Formulae, Genealogical and Interacting Particle Systems with Applications, 2004.

P. , D. Moral, and L. Miclo, Branching and Interacting Particle Systems approximations of Feynman-Kac formulae with applications to nonlinear filtering, Lecture notes in Mathematics, vol.1729, pp.1-145, 2000.

P. , D. Moral, and L. Miclo, Particle approximations of Lyapounov exponents connected to Schrdinger operators and Feynman-Kac semigroups, ESAIM Proba, Stat, vol.7, pp.171-208, 2003.

L. Desvillettes, C. Mouhot, and C. Villani, Celebrating cercignani's conjecture for the boltzmann equation, Kinetic and related models, vol.4, issue.1, pp.277-294, 2011.

L. Desvillettes and C. Villani, On the spatially homogeneous landau equation for hard potentials part ii : h-theorem and applications, Communications in Partial Differential Equations, vol.315, issue.1-2, pp.261-298, 2000.
DOI : 10.1007/s002050050106

P. Diaconis and L. Saloff-coste, Bounds for Kac's Master Equation, Communications in Mathematical Physics, vol.209, issue.3, pp.729-755, 2000.
DOI : 10.1007/s002200050036

E. Dolera, E. Gabetta, and E. Regazzini, Reaching the best possible rate of convergence to equilibrium for solutions of Kac???s equation via central limit theorem, The Annals of Applied Probability, vol.19, issue.1, pp.186-209, 2009.
DOI : 10.1214/08-AAP538

E. Dolera and E. Regazzini, The role of the central limit theorem in discovering sharp rates of convergence to equilibrium for the solution of the Kac equation, The Annals of Applied Probability, vol.20, issue.2, pp.430-461, 2010.
DOI : 10.1214/09-AAP623

E. Dolera and E. Regazzini, Proof of a mckean conjecture on the rate of convergence of boltzmann-equation solutions, Probability Theory and Related Fields, pp.1-75, 2012.

A. Doucet, N. De-freitas, and N. J. Gordon, Sequential Monte-Carlo Methods in Practice, Series Statistics for Engineering and Information Science, 2001.
DOI : 10.1007/978-1-4757-3437-9

S. Duane, A. D. Kennedy, B. J. Pendleton, D. Roweth, and H. Monte-carlo, Hybrid Monte Carlo, Physics Letters B, vol.195, issue.2, pp.216-222, 1987.
DOI : 10.1016/0370-2693(87)91197-X

R. Erban and H. Othmer, From Individual to Collective Behavior in Bacterial Chemotaxis, SIAM Journal on Applied Mathematics, vol.65, issue.2, pp.361-391, 2004.
DOI : 10.1137/S0036139903433232

R. Erban and H. Othmer, : A Paradigm for Multiscale Modeling in Biology, Multiscale Modeling & Simulation, vol.3, issue.2, pp.362-394, 2005.
DOI : 10.1137/040603565

J. Fontbona, H. Guérin, and F. Malrieu, Quantitative estimates for the long time behavior of a PDMP describing the movement of bacteria, ArXiv e-prints, 2010.

E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration: Structure- Preserving Algorithms for Ordinary Differential Equations, 2006.

T. Hillen and H. Othmer, The diffusion limit of transport equations derived from velocityjump processes, SIAM Journal on Applied Mathematics, vol.61, issue.3, pp.751-775, 2000.

A. M. Horowitz, A generalized guided Monte Carlo algorithm, Physics Letters B, vol.268, issue.2, pp.247-252, 1991.
DOI : 10.1016/0370-2693(91)90812-5

URL : http://doi.org/10.1016/0370-2693(91)90812-5

D. Horstman, From 1970 until present: the Keller?Segel model in chemotaxis and its consequences I, Jahresber. Deutsh. Math.-Verein, vol.105, issue.3, pp.103-165, 2003.

D. Horstman, From 1970 until present: the Keller?Segel model in chemotaxis and its consequences II, Jahresber. Deutsh. Math.-Verein, vol.106, issue.2, pp.51-69, 2004.

J. A. Izaguirre and S. S. Hampton, Shadow hybrid Monte Carlo: an efficient propagator in phase space of macromolecules, Journal of Computational Physics, vol.200, issue.2, pp.581-604, 2004.
DOI : 10.1016/j.jcp.2004.04.016

E. Keller and L. Segel, Initiation of slime mold aggregation viewed as an instability, Journal of Theoretical Biology, vol.26, issue.3, pp.399-415, 1970.
DOI : 10.1016/0022-5193(70)90092-5

B. J. Leimkuhler and S. Reich, Simulating Hamiltonian Dynamics, Cambridge Monographs on Applied and Computational Mathematics, vol.14, 2005.
DOI : 10.1017/CBO9780511614118

URL : https://repozitorij.uni-lj.si/Dokument.php?id=39532

P. B. Mackenzie, An improved hybrid Monte Carlo method, Physics Letters B, vol.226, issue.3-4, pp.369-371, 1989.
DOI : 10.1016/0370-2693(89)91212-4

F. Malrieu, Logarithmic sobolev inequalities for some nonlinear pde's, Stochastic processes and their applications, pp.109-132, 2001.
DOI : 10.1016/s0304-4149(01)00095-3

URL : http://doi.org/10.1016/s0304-4149(01)00095-3

B. Mao and A. R. Friedman, Molecular dynamics simulation by atomic mass weighting, Biophysical Journal, vol.58, issue.3, pp.803-805, 1990.
DOI : 10.1016/S0006-3495(90)82424-3

URL : http://doi.org/10.1016/s0006-3495(90)82424-3

S. Mischler and C. Mouhot, About Kac??s program in kinetic theory, Comptes Rendus Mathematique, vol.349, issue.23-24, pp.1245-1250, 2011.
DOI : 10.1016/j.crma.2011.11.012

URL : http://arxiv.org/abs/1111.3472

C. Mouhot, Rate of Convergence to Equilibrium for the Spatially Homogeneous Boltzmann Equation with Hard Potentials, Communications in Mathematical Physics, vol.261, issue.3, pp.629-672, 2006.
DOI : 10.1007/s00220-005-1455-x

URL : https://hal.archives-ouvertes.fr/hal-00076709

R. Oliveira, On the convergence to equilibrium of Kac???s random walk on matrices, The Annals of Applied Probability, vol.19, issue.3, pp.1200-1231, 2009.
DOI : 10.1214/08-AAP550

H. Othmer, W. Dunbar, and . Alt, Models of dispersal in biological systems, Journal of Mathematical Biology, vol.25, issue.3, pp.263-298, 1988.
DOI : 10.1007/BF00277392

H. Othmer and T. Hillen, The Diffusion Limit of Transport Equations II: Chemotaxis Equations, SIAM Journal on Applied Mathematics, vol.62, issue.4, pp.1222-1250, 2002.
DOI : 10.1137/S0036139900382772

C. Patlak, Random walk with persistence and external bias, The Bulletin of Mathematical Biophysics, vol.198, issue.3, pp.311-338, 1953.
DOI : 10.1007/BF02476407

S. Reich, Smoothed dynamics of highly oscillatory Hamiltonian systems, Physica D: Nonlinear Phenomena, vol.89, issue.1-2, pp.28-42, 1995.
DOI : 10.1016/0167-2789(95)00212-X

S. Reich, Smoothed Langevin dynamics of highly oscillatory systems, Physica D: Nonlinear Phenomena, vol.138, issue.3-4, pp.210-224, 2000.
DOI : 10.1016/S0167-2789(99)00200-6

M. Rousset, On the Control of an Interacting Particle Estimation of Schr??dinger Ground States, SIAM Journal on Mathematical Analysis, vol.38, issue.3, pp.824-844, 2006.
DOI : 10.1137/050640667

H. Rubin and P. Ungar, Motion under a strong constraining force, Communications on Pure and Applied Mathematics, vol.9, issue.1, pp.65-87, 1957.
DOI : 10.1002/cpa.3160100103

J. Saragosti, V. Calvez, N. Bournaveas, A. Buguin, P. Silberzan et al., Mathematical Description of Bacterial Traveling Pulses, PLoS Computational Biology, vol.33, issue.8, p.1000890, 2010.
DOI : 10.1371/journal.pcbi.1000890.s001

URL : https://hal.archives-ouvertes.fr/hal-00440108

A. Stock, A nonlinear stimulus-response relation in bacterial chemotaxis, Proceedings of the National Academy of Sciences, vol.96, issue.20, pp.10945-10947, 1999.
DOI : 10.1073/pnas.96.20.10945

A. Sznitman, Brownian motion, obstacles and random media, 1998.
DOI : 10.1007/978-3-662-11281-6

F. Takens, Motion under the influence of a strong constraining force, Global theory of dynamical systems (Proc. Internat. Conf., Northwestern Univ, pp.425-445, 1979.
DOI : 10.2307/1971029

H. Tanaka, Probabilistic treatment of the boltzmann equation of maxwellian molecules, Probability Theory and Related Fields, pp.67-105, 1978.

G. Toscani and C. Villani, Sharp Entropy Dissipation Bounds and Explicit Rate of Trend to Equilibrium for the Spatially Homogeneous Boltzmann Equation, Communications in Mathematical Physics, vol.203, issue.3, pp.667-706, 1999.
DOI : 10.1007/s002200050631

J. Toulouse, R. Assaraf, and C. J. Umrigar, Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density, The Journal of Chemical Physics, vol.126, issue.24, p.244112, 2007.
DOI : 10.1063/1.2746029

URL : https://hal.archives-ouvertes.fr/hal-00979441

J. Toulouse and C. J. Umrigar, Optimization of quantum Monte Carlo wave functions by energy minimization, The Journal of Chemical Physics, vol.126, issue.8, p.84102, 2007.
DOI : 10.1063/1.2437215

URL : https://hal.archives-ouvertes.fr/hal-00981188

C. J. Umrigar and C. Filippi, Energy and Variance Optimization of Many-Body Wave Functions, Physical Review Letters, vol.94, issue.15, p.150201, 2005.
DOI : 10.1103/PhysRevLett.94.150201

N. G. Van-kampen, Elimination of fast variables, Physics Reports, vol.124, issue.2, pp.9-160, 1985.
DOI : 10.1016/0370-1573(85)90002-X

C. Villani, A review of mathematical topics in collisional kinetic theory, Handbook of mathematical fluid dynamics, pp.71-74, 2002.

C. Villani, Cercignani's Conjecture is Sometimes True and Always Almost True, Communications in Mathematical Physics, vol.234, issue.3, pp.455-490, 2003.
DOI : 10.1007/s00220-002-0777-1

C. Villani, Topics in Optimal Transportation, Graduate Studies in Mathematics, vol.58, 2003.
DOI : 10.1090/gsm/058

M. Von-renesse and K. Sturm, Transport inequalities, gradient estimates, entropy and Ricci curvature, Communications on Pure and Applied Mathematics, vol.108, issue.7, pp.923-940, 2005.
DOI : 10.1002/cpa.20060

C. Xue and H. G. Othmer, Multiscale Models of Taxis-Driven Patterning in Bacterial Populations, SIAM Journal on Applied Mathematics, vol.70, issue.1, pp.133-167, 2009.
DOI : 10.1137/070711505