Point configurations: from statistical physics to potential theory / Configurations de points : de la physique statistique à la théorie du potentiel

Collection Point configurations: from statistical physics to potential theory / Configurations de points : de la physique statistique à la théorie du potentiel

Organisateur(s) Aistleitner, Christoph ; Behrend, Kai ; Bilyk, Dmitriy ; Chafaï, Djalil ; Etayo, Ujué ; Grabner, Peter ; Kuijlaars, Arno ; Maïda, Mylène ; Radchenko, Danylo ; Serfaty, Sylvia

Date(s) 04/05/2026 - 08/05/2026

URL associée https://conferences.cirm-math.fr/3455.html

00:00:00 / 00:00:00

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Computational statistical physics

De Manon Michel

This one-hour introductory course surveys core ideas in computational statistical mechanics through the lens of stochastic sampling algorithms. Beginning with classical Monte Carlo methods and the foundations of Markov chain Monte Carlo (MCMC), the course introduces global and detailed balances, ergodicity, and practical sampling strategies for equilibrium systems. It then discusses quantitative diagnostics for convergence and mixing, including autocorrelation times and spectral considerations. The course concludes with modern approaches to accelerating sampling by moving beyond reversible dynamics toward non-reversible Markov processes, highlighting how broken detailed balance and irreversible flows can substantially improve convergence efficiency in high-dimensional and metastable systems.

Informations sur la vidéo

Date de captation 05/05/2026
Date de publication 01/06/2026
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Luca Recanzone
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20479703
Citer cette vidéo Michel, Manon (05/05/2026). Computational statistical physics. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20479703
URL https://dx.doi.org/10.24350/CIRM.V.20479703

Domaine(s)

Mécanique statistique

Bibliographie

FRENKEL, Daan et SMIT, Berend. Understanding molecular simulation: from algorithms to applications. elsevier, 2023. - https://doi.org/10.1016/C2009-0-63921-0
DIACONIS, Persi, HOLMES, Susan, et NEAL, Radford M. Analysis of a nonreversible Markov chain sampler. Annals of Applied Probability, 2000, p. 726-752. - https://doi.org/10.1214/aoap/1019487508
DIACONIS, Persi, LEBEAU, Gilles, et MICHEL, Laurent. Geometric analysis for the Metropolis algorithm on Lipschitz domains. Inventiones mathematicae, 2011, vol. 185, no 2, p. 239-281. - https://doi.org/10.1007/s00222-010-0303-6
EBERLE, Andreas, GUILLIN, Arnaud, HAHN, Leo, et al. Convergence of non-reversible Markov processes via lifting and flow Poincar {\'e} inequality. arXiv preprint arXiv:2503.04238, 2025. - https://doi.org/10.48550/arXiv.2503.04238
EDWARDS, Robert G. et SOKAL, Alan D. Generalization of the fortuin-kasteleyn-swendsen-wang representation and monte carlo algorithm. Physical review D, 1988, vol. 38, no 6, p. 2009. - https://doi.org/10.1103/PhysRevD.38.2009
HASTINGS, W. Keith. Monte Carlo sampling methods using Markov chains and their applications. 1970. - https://doi.org/10.1093/biomet/57.1.97
LEVIN, David A. et PERES, Yuval. Markov chains and mixing times. American Mathematical Soc., 2017. - https://doi.org/10.1090/mbk/107
LU, Jianfeng et WANG, Lihan. On explicit L 2-convergence rate estimate for piecewise deterministic Markov processes in MCMC algorithms. The Annals of Applied Probability, 2022, vol. 32, no 2, p. 1333-1361. - https://doi.org/10.1214/21-AAP1710
METROPOLIS, Nicholas, ROSENBLUTH, Arianna W., ROSENBLUTH, Marshall N., et al. Equation of state calculations by fast computing machines. The journal of chemical physics, 1953, vol. 21, no 6, p. 1087-1092. - [http:// https://doi.org/10.1063/1.1699114](http:// https://doi.org/10.1063/1.1699114)
MICHEL, Manon, KAPFER, Sebastian C., et KRAUTH, Werner. Generalized event-chain Monte Carlo: Constructing rejection-free global-balance algorithms from infinitesimal steps. The Journal of chemical physics, 2014, vol. 140, no 5. - https://doi.org/10.1063/1.4863991
MONEMVASSITIS, Athina, GUILLIN, Arnaud, et MICHEL, Manon. PDMP characterisation of event-chain Monte Carlo algorithms for particle systems. arXiv preprint arXiv:2208.11070, 2022. - https://doi.org/10.1007/s10955-023-03069-8
NEAL, Radford M. Bayesian learning for neural networks. Springer Science & Business Media, 2012. - https://doi.org/10.1007/978-1-4612-0745-0
SWENDSEN, Robert H. et WANG, Jian-Sheng. Nonuniversal critical dynamics in Monte Carlo simulations. Physical review letters, 1987, vol. 58, no 2, p. 86. - https://doi.org/10.1103/PhysRevLett.58.86
WOLFF, Ulli. Collective Monte Carlo updating for spin systems. Physical Review Letters, 1989, vol. 62, no 4, p. 361. - https://doi.org/10.1103/PhysRevLett.62.361

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