M. De-buffon,

, Histoire naturelle générale et particulière, 1753.

J. Neumann, Various techniques used in connection with random digits, The Monte Carlo Method, Number 12 in National Bureau of Standards Applied Mathematics Series, pp.36-38, 1951.

N. Metropolis and &. S. Ulam, The Monte Carlo Method, Journal of the American statistical association, vol.44, pp.335-341, 1949.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, and A. H. , Teller & E. Teller; Equation of State Calculations by Fast Computing Machines, J. Chem. Phys, vol.21, pp.1087-1092, 1953.

W. Krauth, Statistical Mechanics: Algorithms and Computations, 2006.

B. L. Hammond, W. A. Lester-&-p, and . Reynolds,

, Monte Carlo methods in ab initio quantum chemistry, vol.1, 1994.

B. F. Manly,

, Randomization, bootstrap and Monte Carlo methods in biology, 2006.

C. Andrieu, N. Freitas, A. I. Doucet-&-m, and . Jordan, An Introduction to MCMC for Machine Learning; Machine Learning 50, pp.5-43, 2003.

E. P. Bernard, W. &. Krauth, and . Wilson, Event-chain Monte Carlo algorithms for hard-sphere systems, Phys. Rev. E, vol.80, p.56704, 2009.

M. Michel, S. C. Kapfer, and &. Krauth, Generalized event-chain Monte Carlo: Constructing rejection-free global-balance algorithms from infinitesimal steps

, J. Chem. Phys, vol.140, p.54116, 2014.

M. Michel, J. Mayer, and &. Krauth, Event-chain Monte Carlo for classical continuous spin models, Europhysics Letters), vol.112, p.20003, 2015.

Z. Lei and &. Krauth, Irreversible Markov chains in spin models: Topological excitations, Europhysics Letters), vol.121, p.10008, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01763479

E. P. Bernard and &. Krauth, Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition, Phys. Rev. Lett, vol.107, p.155704, 2011.

M. Engel, J. A. Anderson, S. C. Glotzer, M. Isobe, E. P. Bernard et al.,

, Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods, Phys. Rev. E, vol.87, p.42134, 2013.

S. C. Kapfer and &. Krauth, Two-Dimensional Melting: From Liquid-Hexatic Coexistence to Continuous Transitions, Phys. Rev. Lett, vol.114, p.35702, 2015.

M. F. Faulkner, L. Qin, A. C. Maggs, and &. Krauth, All-atom computations with irreversible Markov chains, J. Chem. Phys, vol.149, p.64113, 2018.
DOI : 10.1063/1.5036638

Z. Lei and &. Krauth, Mixing and perfect sampling in one-dimensional particle systems, Europhysics Letters), vol.124, p.20003, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01950833

S. C. Kapfer and &. Krauth, Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium, Phys. Rev. Lett, vol.119, p.240603, 2017.
DOI : 10.1103/physrevlett.119.240603

URL : http://arxiv.org/pdf/1705.06689

P. Erd? and &. A. Rényi, On a classical problem of probability theory, 1961.

Z. Lei, W. &. Krauth, and . Maggs, Event-chain Monte Carlo with factor fields, 2018.

A. Markov, Extension of the law of large numbers to quantities, depending on each other (1906). Reprint, 2006.

A. Einstein, Investigations on the Theory of the Brownian Movement, 1956.

A. N. Kolmogorov, Foundations of the Theory of Probability: Second English Edition, 2018.

P. Laplace, Pierre-Simon Laplace Philosophical Essay on Probabilities: Translated from the fifth French edition of 1825 With Notes, vol.13, 2012.

, A. N. Shiryaev; Probability-1, vol.1

, Graduate Texts in Mathematics, vol.95, pp.978-978, 2016.

B. V. Gnedenko, A. N. Kolmogorov, K. L. Chung, and &. L. Doob, Limit Distributions for Sums of Independent Random Variables, 1968.

L. De-haan and &. A. Ferreira, Extreme Value Theory: An Introduction, 2007.

P. Lévy, Sur certains processus stochastiques homogènes, Compos. Math, vol.7, pp.283-339, 1939.

A. Y. Khinchin, Theory of correlation of stationary stochastic processes; Uspekhi matematicheskikh nauk pp, pp.42-51, 1938.

M. Fréchet, Sur la loi de probabilite de l'écart maximum, Ann. Soc. Math. Polon, vol.6, pp.93-116, 1927.

R. A. Fisher-&-l and . Tippett, Limiting forms of the frequency distribution of the largest or smallest member of a sample, Mathematical Proceedings of the Cambridge Philosophical Society, vol.24, pp.180-190, 1928.

B. Gnedenko, Sur la distribution limite du terme maximum d'une série aléa-toire, pp.423-453, 1943.

G. Grimmett and &. Stirzaker, Probability and random processes, 2001.

E. Ising, Beitrag zur theorie des ferromagnetismus, Zeitschrift für Physik, vol.31, pp.253-258, 1925.

C. D. Meyer, Matrix analysis and applied linear algebra, vol.71, 2000.

D. A. Levin, Y. &. Peres, and . Wilmer, Markov Chains and Mixing Times, 2008.

A. ,

, Monte Carlo methods in statistical mechanics: foundations and new algorithms, pp.131-192, 1997.

D. &. Aldous and . Fill, Reversible markov chains and random walks on graphs, recompiled, 2002.

P. Diaconis, The cutoff phenomenon in finite Markov chains, Proceedings of the National Academy of Sciences, vol.93, pp.1659-1664, 1996.

P. Flajolet, D. Gardy, and &. Thimonier, Birthday paradox, coupon collectors, caching algorithms and self-organizing search, Discrete Applied Mathematics, vol.39, pp.207-229, 1992.
URL : https://hal.archives-ouvertes.fr/inria-00075832

D. Williams, Probability with martingales, 1991.

N. Berestycki, Lectures on mixing times, 2014.

G. Pólya, Über eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt im Straßennetz

, Mathematische Annalen, vol.84, pp.149-160, 1921.

H. Lacoin, The simple exclusion process on the circle has a diffusive cutoff window

, Ann. Inst. H. Poincaré Probab. Statist, vol.53, pp.1402-1437, 2017.

B. Morris, The mixing time for simple exclusion

, Ann. Appl. Probab, vol.16, pp.615-635, 2006.

M. Gorissen, A. Lazarescu, K. Mallick, and &. Vanderzande, Exact Current Statistics of the Asymmetric Simple Exclusion Process with Open Boundaries, Phys. Rev. Lett, vol.109, p.170601, 2012.

L. Gwa and &. Spohn, Six-vertex model, roughened surfaces, and an asymmetric spin Hamiltonian, Phys. Rev. Lett, vol.68, pp.725-728, 1992.

A. Lazarescu and &. Mallick, An exact formula for the statistics of the current in the TASEP with open boundaries, J. Phys. A, vol.44, p.315001, 2011.

T. Chou, K. K. Mallick-&-r, and . Zia, Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport, Rep. Prog. Phys, vol.74, p.116601, 2011.

J. Baik and &. Liu, TASEP on a Ring in Sub-relaxation

, J. Stat. Phys, vol.165, pp.1051-1085, 2016.

D. Randall and &. Winkler, Mixing Points on an Interval, Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithmics and Combinatorics, ALENEX /ANALCO 2005, pp.218-221, 2005.

D. Randall and &. Winkler, Algorithms and Techniques: 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th International Workshop on Randomization and Computation, RANDOM 2005, pp.426-435, 2005.

L. Wasserman, All of Statistics: A Concise Course in Statistical Inference, Statistics, p.9780387402727, 2003.

J. W. Gibbs, Charles Scribner's sons, Elementary principles in statistical mechanics, 1902.

W. K. Hastings,

, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, vol.57, pp.97-109, 1970.

A. A. Barker,

, Monte carlo calculations of the radial distribution functions for a proton-electron plasma, Australian Journal of Physics, vol.18, pp.119-134, 1965.

W. Janke,

, Multicanonical Monte Carlo simulations, Physica A: Statistical Mechanics and its Applications, vol.254, pp.164-178, 1998.

P. C. Hohenberg-&-b and . Halperin, Theory of dynamic critical phenomena, Rev. Mod. Phys, vol.49, pp.435-479, 1977.

R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, and &. Troyansky, Determining computational complexity from characteristic 'phase transitions', Nature, vol.400, p.133, 1999.

L. Onsager, Crystal Statistics. I. A Two-Dimensional Model with an OrderDisorder Transition, Phys. Rev, vol.65, pp.117-149, 1944.

R. H. Swendsen and &. Wang, Nonuniversal critical dynamics in Monte Carlo simulations, Phys. Rev. Lett, vol.58, pp.86-88, 1987.

C. Fortuin-&-p.-kasteleyn, On the random-cluster model: I. Introduction and relation to other models, Physica, vol.57, pp.536-564, 1972.

U. Wolff, Collective Monte Carlo Updating for Spin Systems, Phys. Rev. Lett, vol.62, pp.361-364, 1989.

J. Villain, Theory of one-and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet, Journal de Physique, vol.36, pp.581-590, 1975.
URL : https://hal.archives-ouvertes.fr/jpa-00208289

W. Janke and &. Nather, High-precision Monte Carlo study of the twodimensional XY Villain model, Phys. Rev. B, vol.48, pp.7419-7433, 1993.

T. Obuchi and &. Kawamura,

, Monte Carlo simulations of the three-dimensional XY spin glass focusing on chiral and spin order, Phys. Rev. B, vol.87, p.174438, 2013.

P. Kasteleyn, The statistics of dimers on a lattice: I. The number of dimer arrangements on a quadratic lattice, Physica, vol.27, pp.1209-1225, 1961.

W. Krauth-&-r and . Moessner, Pocket Monte Carlo algorithm for classical doped dimer models, Phys. Rev. B, vol.67, p.64503, 2003.

C. Dress and &. Krauth, Cluster algorithm for hard spheres and related systems

, J. Phys. A, vol.28, pp.597-601, 1995.

L. Santen and &. Krauth, Absence of Thermodynamic Phase Transition in a Model Glass Former, Nature, vol.405, pp.550-551, 2000.

D. J. Earl-&-m and . Deem, Parallel tempering: Theory, applications, and new perspectives, Phys. Chem. Chem. Phys, vol.7, pp.3910-3916, 2005.

L. Wang, Discovering phase transitions with unsupervised learning

, Phys. Rev. B, vol.94, p.195105, 2016.

P. Diaconis, S. M. Holmes-&-r, and . Neal, Analysis of a nonreversible Markov chain sampler

, Ann. Appl. Probab, vol.10, pp.726-752, 2000.

C. J. O'keeffe and &. G. Orkoulas, Parallel canonical Monte Carlo simulations through sequential updating of particles, J. Chem. Phys, vol.130, p.134109, 2009.

M. Michel, Irreversible Markov chains by the factorized Metropolis filter: Algorithms and applications in particle systems and spin models; Theses, 2016.

K. S. Turitsyn, M. Chertkov, and &. Vucelja, Irreversible Monte Carlo algorithms for efficient sampling, Physica D: Nonlinear Phenomena, vol.240, pp.410-414, 2011.

E. Bernard, Algorithms and applications of the Monte Carlo method: Two-dimensional melting and perfect sampling; Theses

E. A. Peters and &. De-with, Rejection-free Monte Carlo sampling for general potentials, Phys. Rev. E, vol.85, p.26703, 2012.

A. Bortz, M. Kalos, and &. Lebowitz, A new algorithm for Monte Carlo simulation of Ising spin systems, Journal of Computational Physics, vol.17, pp.10-18, 1975.

A. Sinclair and &. Jerrum, Approximate counting, uniform generation and rapidly mixing Markov chains, pp.93-133, 1989.

A. Sinclair, Improved Bounds for Mixing Rates of Markov Chains and Multicommodity Flow

, Combinatorics, Probability and Computing, vol.1, pp.351-370, 1992.

F. Chen, L. Lovász, and &. Pak, Lifting Markov Chains to Speed up Mixing, Proceedings of the 17th Annual ACM Symposium on Theory of Computing p, p.275, 1999.

M. J. Lighthill, An introduction to Fourier analysis and generalised functions, 1958.

B. J. Alder-&-t and . Wainwright,

, Phys. Rev, vol.127, pp.359-361, 1962.

N. D. Mermin, Crystalline Order in Two Dimensions, Phys. Rev, vol.176, pp.250-254, 1968.

J. M. Kosterlitz-&-d and . Thouless, Long range order and metastability in two dimensional solids and superfluids. (Application of dislocation theory)

, J. Phys. C, vol.5, pp.124-126, 1972.

B. I. Halperin-&-d and . Nelson,

, Phys. Rev. Lett, vol.41, pp.121-124, 1978.

A. P. Young, Melting and the vector Coulomb gas in two dimensions

, Phys. Rev. B, vol.19, pp.1855-1866, 1979.

Y. Nishikawa, M. Michel, W. Krauth, and &. Hukushima, Event-chain algorithm for the Heisenberg model: Evidence for z 1 dynamic scaling, Phys. Rev. E, vol.92, p.63306, 2015.

C. Kittel-&-p.-mceuen, Introduction to solid state physics, vol.8, 1996.

J. M. Kosterlitz-&-d and . Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C, vol.6, pp.1181-1203, 1973.

M. Hasenbusch, The two-dimensional XY model at the transition temperature: a high-precision Monte Carlo study, J. Phys. A, vol.38, pp.5869-5883, 2005.

C. Holm and &. Janke,

, Monte Carlo study of topological defects in the 3D Heisenberg model, J. Phys. A, vol.27, pp.2553-2563, 1994.

N. D. Mermin and &. Wagner, Absence of Ferromagnetism or Antiferromagnetism in One-or Two-Dimensional Isotropic Heisenberg Models, Phys. Rev. Lett, vol.17, pp.1133-1136, 1966.

M. Mézard, G. Parisi, and &. Virasoro, Spin glass theory and beyond: An Introduction to the Replica Method and Its Applications, vol.9, 1987.

J. M. Kosterlitz, Phase Transitions in Long-Range Ferromagnetic Chains, Phys. Rev. Lett, vol.37, pp.1577-1580, 1976.

F. Wegner, Spin-ordering in a planar classical Heisenberg model, pp.465-470, 1967.

J. Fröhlich and &. T. Spencer, The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas, vol.81, pp.527-602, 1981.

B. Jancovici, Infinite Susceptibility Without Long-Range Order: The TwoDimensional Harmonic "Solid", Phys. Rev. Lett, vol.19, pp.20-22, 1967.

M. Aizenman and &. B. Simon, A comparison of plane rotor and Ising models

, Physics Letters A, vol.76, pp.281-282, 1980.

C. H. Papadimitriou and &. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, 1982.

B. Berg and &. Lüscher, Definition and statistical distributions of a topological number in the lattice O(3) -model, Nuclear Physics B, vol.190, pp.412-424, 1981.

S. Ostlund, Interactions between topological point singularities, Phys. Rev. B, vol.24, pp.485-488, 1981.

M. Lau and &. Dasgupta, Role of topological defects in the phase transition of the three-dimensional Heisenberg model, J. Phys. A, vol.21, pp.51-57, 1988.

L. Tonks, The Complete Equation of State of One, Two and Three-Dimensional Gases of Hard Elastic Spheres, Phys. Rev, vol.50, p.955, 1936.

K. Kimura and &. S. Higuchi, Anomalous diffusion analysis of the lifting events in the event-chain Monte Carlo for the classical XY models, Europhysics Letters), vol.120, p.30003, 2017.

R. Peierls, On Ising's model of ferromagnetism

, Mathematical Proceedings of the Cambridge Philosophical Society, vol.32, pp.477-481, 1936.

C. Banderier and &. Wallner, Local time for lattice paths and the associated limit laws, Proceedings of the 11th International Conference on Random and Exhaustive Generation of Combinatorial Structures, vol.2113, pp.69-78, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01796320

W. Feller, An introduction to probability theory and its applications, 1968.

J. M. Kosterlitz and D. J. Thouless, J. Phys. C, vol.6, p.1181, 1973.

U. Wolff, Phys. Rev. Lett, vol.62, p.361, 1989.

M. Hasenbusch, J. Phys. A, vol.38, p.5869, 2005.

C. Holm and W. Janke, J. Phys. A, vol.27, p.2553, 1994.

E. P. Bernard, W. Krauth, and D. B. Wilson, Phys. Rev. E, vol.80, p.56704, 2009.

M. Michel, S. C. Kapfer, and W. Krauth, J. Chem. Phys, vol.140, p.54116, 2014.

P. Diaconis, S. Holmes, and R. M. Neal, Ann. Appl. Probab, vol.10, p.726, 2000.

E. P. Bernard and W. Krauth, Phys. Rev. Lett, vol.107, p.155704, 2011.

S. C. Kapfer and W. Krauth, Phys. Rev. Lett, vol.114, p.35702, 2015.

J. Harland, M. Michel, T. A. Kampmann, and J. Kierfeld, EPL, p.30001, 2017.

M. Michel, J. Mayer, and W. Krauth, EPL, p.112, 2015.

K. Kimura and S. Higuchi, EPL, p.30003, 2017.

Y. Nishikawa, M. Michel, W. Krauth, and K. Hukushima, Phys. Rev. E, vol.92, p.63306, 2015.

F. Wegner, Z. Phys, vol.206, p.465, 1967.

D. A. Levin, Y. Peres, and E. L. Wilmer, Markov Chains and Mixing Times, 2008.
DOI : 10.1090/mbk/058

C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, 1982.

L. De-haan and A. Ferreira, Extreme Value Theory: An Introduction, 2007.

B. Berg and M. Lüscher, Nucl. Phys. B, vol.190, p.412, 1981.

M. Lau and C. Dasgupta, J. Phys. A, vol.21, p.51, 1988.

S. Ostlund, Phys. Rev. B, vol.24, p.485, 1981.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys, vol.21, p.1087, 1953.

L. Devroye, Non-Uniform Random Variate Generation, 1986.
DOI : 10.1007/978-1-4613-8643-8

W. Krauth, Statistical Mechanics: Algorithms and Computations, 2006.

F. Martinelli, Lectures on Glauber Dynamics for Discrete Spin Models,i nLectures on Probability Theory and Statistics: Ecole d'Etéd eP r o b a b i l i t ´ es de Saint-Flour XXVII -1997, pp.93-191, 1999.

E. Lubetzky and A. Sly, Commun. Math. Phys, vol.313, p.815, 2012.

D. A. Levin, Y. Peres, and E. L. Wilmer, Markov Chains and Mixing Time, 2008.

P. Diaconis, J. Stat. Phys, vol.144, p.445, 2011.

B. A. Berg, Markov Chain Monte Carlo Simulations and Their Statistical Analysis: With Web-based Fortran Code, 2004.
DOI : 10.1142/5602

D. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, 2013.

J. G. Propp, D. B. Wilson, and R. Struct, Algorithms, vol.9, p.223, 1996.

K. S. Turitsyn, M. Chertkov, M. Vucelja, and D. Physica, , vol.240, p.410, 2011.

H. C. Fernandes and M. Weigel, Comput. Phys. Commun, vol.182, p.1856, 2011.

E. P. Bernard, W. Krauth, and D. B. Wilson, Phys. Rev. E, vol.80, p.56704, 2009.

M. Michel, S. C. Kapfer, and W. Krauth, J. Chem. Phys, vol.140, p.54116, 2014.

S. C. Kapfer and W. Krauth, Phys. Rev. Lett, vol.119, p.240603, 2017.

E. P. Bernard and W. Krauth, Phys. Rev. Lett, vol.107, p.155704, 2011.

Z. Lei and W. Krauth, EPL, p.10008, 2018.

T. A. Kampmann, H. Boltz, and J. Kierfeld, J. Chem. Phys, vol.143, p.44105, 2015.

J. Harland, M. Michel, T. A. Kampmann, and J. Kierfeld, EPL, p.30001, 2017.

M. F. Faulkner, L. Qin, A. C. Maggs, and W. Krauth, J. Chem. Phys, vol.149, p.64113, 2018.

S. C. Kapfer and W. Krauth, Phys. Rev. E, vol.94, p.31302, 2016.

P. Diaconis, S. Holmes, and R. M. Neal, Ann. Appl. Probab, vol.10, p.726, 2000.

D. Randall and P. Winkler, Mixing Points on an Interval,i nProceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithmics and Combinatorics, ALENEX/ANALCO 2005, p.22

D. Randall and P. Winkler, Mixing Points on a Circle, Lect. Notes Comput. Sci, vol.3624, pp.426-435, 2005.
DOI : 10.1007/11538462_36

H. Lacoin, Ann. Inst. H. Poincaré Probab. Stat, vol.53, p.1402, 2017.

L. Gwa and H. Spohn, Phys. Rev. Lett, vol.68, p.725, 1992.

T. Chou, K. Mallick, and R. K. Zia, Rep. Prog. Phys, vol.74, p.116601, 2011.

J. Baik and Z. Liu, J. Stat. Phys, vol.165, p.1051, 2016.

D. B. Wilson and R. Struct, Algorithms, vol.16, p.85, 2000.

R. Kannan, M. W. Mahoney, and R. Montenegro, Rapid mixing of several Markov chains for a hard-core model,i n14th Annual ISAAC, Lect. Notes Comput. Sci, pp.663-675, 2003.

P. Erdos, A. Rényi, and M. Tud, Akad. Mat. Kutató Int. Közl, vol.6, p.215, 1961.

G. Blom, L. Holst, and D. Sandell, Problems and Snapshots from the World of Probability, 1994.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of State Calculations by Fast Computing Machines, J. Chem. Phys, vol.21, pp.1087-1092, 1953.
DOI : 10.2172/4390578

D. A. Levin, Y. Peres, and E. L. Wilmer, Markov Chains and Mixing Times, 2008.
DOI : 10.1090/mbk/058

W. Krauth, Statistical Mechanics: Algorithms and Computations, 2006.

B. J. Alder and T. E. Wainwright, Phase Transition for a Hard Sphere System, J. Chem. Phys, vol.27, pp.1208-1209, 1957.

K. S. Turitsyn, M. Chertkov, and M. Vucelja, Irreversible Monte Carlo algorithms for efficient sampling, Physica D: Nonlinear Phenomena, vol.240, issue.4-5, pp.410-414, 2011.

Y. Sakai and K. Hukushima, Dynamics of OneDimensional Ising Model without Detailed Balance Condition, Journal of the Physical Society of Japan, vol.82, issue.6, p.64003, 2013.

Y. Sakai and K. Hukushima, Eigenvalue analysis of an irreversible random walk with skew detailed balance conditions, Phys. Rev. E, vol.93, p.43318, 2016.

J. Bierkens, A. Bouchard-côté, A. Doucet, A. B. Duncan, P. Fearnhead et al., Piecewise deterministic Markov processes for scalable Monte Carlo on restricted domains, Statistics & Probability Letters, vol.136, pp.148-154, 2018.

E. P. Bernard, W. Krauth, and D. B. Wilson, Eventchain Monte Carlo algorithms for hard-sphere systems, Phys. Rev. E, vol.80, p.56704, 2009.

M. Michel, S. C. Kapfer, and W. Krauth, Generalized event-chain monte carlo: Constructing rejection-free global-balance algorithms from infinitesimal steps, J. Chem. Phys, vol.140, issue.5, p.54116, 2014.

E. P. Bernard and W. Krauth, Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition, Phys. Rev. Lett, vol.107, p.155704, 2011.

M. Engel, J. A. Anderson, S. C. Glotzer, M. Isobe, E. P. Bernard et al., Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods, Phys. Rev. E, vol.87, p.42134, 2013.

S. C. Kapfer and W. Krauth, Two-Dimensional Melting: From Liquid-Hexatic Coexistence to Continuous Transitions, Phys. Rev. Lett, vol.114, p.35702, 2015.

M. Michel, J. Mayer, and W. Krauth, Event-chain Monte Carlo for classical continuous spin models, EPL, vol.112, issue.2, p.20003, 2015.

Y. Nishikawa, M. Michel, W. Krauth, and K. Hukushima, Event-chain algorithm for the heisenberg model: Evidence for z 1 dynamic scaling, Phys. Rev. E, vol.92, p.63306, 2015.

M. Hasenbusch and S. Schaefer, Testing the event-chain algorithm in asymptotically free models, Phys. Rev. D, vol.98, p.54502, 2018.

S. C. Kapfer and W. Krauth, Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium, Phys. Rev. Lett, vol.119, p.240603, 2017.

Z. Lei and W. Krauth, Mixing and perfect sampling in one-dimensional particle systems, EPL, vol.124, issue.2, p.20003, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01950833

D. Randall and P. Winkler, Mixing Points on an Interval, Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithmics and Combinatorics, ALENEX /ANALCO 2005, pp.218-221, 2005.

D. Randall and P. Winkler, Mixing Points on a Circle, Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques: 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th International Workshop on Randomization and Computation, RANDOM 2005, pp.426-435, 2005.

Z. Lei and W. Krauth, Irreversible Markov chains in spin models: Topological excitations, EPL, vol.121, p.10008, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01763479

M. F. Faulkner, L. Qin, A. C. Maggs, and W. Krauth, All-atom computations with irreversible Markov chains, J. Chem. Phys, vol.149, issue.6, p.64113, 2018.

A. C. Maggs, Multiscale Monte Carlo Algorithm for Simple Fluids, Phys. Rev. Lett, vol.97, p.197802, 2006.

E. A. Peters and G. De-with, Rejection-free Monte Carlo sampling for general potentials, Phys. Rev. E, vol.85, p.26703, 2012.

J. Harland, M. Michel, T. A. Kampmann, and J. Kierfeld, Event-chain Monte Carlo algorithms for threeand many-particle interactions, EPL, vol.117, issue.3, p.30001, 2017.
DOI : 10.1209/0295-5075/117/30001

URL : http://iopscience.iop.org/article/10.1209/0295-5075/117/30001/pdf

B. J. Alder and T. E. Wainwright, Decay of the Velocity Autocorrelation Function, Phys. Rev. A, vol.1, pp.18-21, 1970.

J. P. Wittmer, P. Poli´nskapoli´nska, H. Meyer, J. Farago, A. Johner et al., Scalefree center-of-mass displacement correlations in polymer melts without topological constraints and momentum conservation: A bond-fluctuation model study, J. Chem. Phys, vol.134, issue.23, pp.234901-234901, 2011.

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

H. Flyvbjerg and H. G. Petersen, Error estimates on averages of correlated data, J. Chem. Phys, vol.91, issue.1, pp.461-466, 1989.

Y. Hu and P. Charbonneau, Clustering and assembly dynamics of a one-dimensional microphase former, Soft Matter, vol.14, issue.20, pp.4101-4109, 2018.

T. R. Scavo and J. B. Thoo, On the Geometry of Halley's Method, The American Mathematical Monthly, vol.102, issue.5, pp.417-426, 1995.

S. C. Kapfer and W. Krauth, Cell-veto Monte Carlo algorithm for long-range systems, Phys. Rev. E, vol.94, p.31302, 2016.
DOI : 10.1103/physreve.94.031302

URL : http://arxiv.org/pdf/1606.06780

L. Tonks, The Complete Equation of State of One, Two and Three-Dimensional Gases of Hard Elastic Spheres, Phys. Rev, vol.50, p.955, 1936.

K. Kimura and S. Higuchi, Anomalous diffusion analysis of the lifting events in the event-chain Monte Carlo for the classical XY models, EPL, vol.120, issue.3, p.30003, 2017.

W. Feller, An introduction to probability theory and its applications, vol.I, 1968.

C. Banderier and M. Wallner, Local time for lattice paths and the associated limit laws, Proceedings of the 11th International Conference on Random and Exhaustive Generation of Combinatorial Structures, vol.2113, pp.69-78, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01796320

D. C. Wallace, Thermoelastic Theory of Stressed Crystals and Higher-Order Elastic Constants, vol.25, pp.301-404, 1970.