ECMC 2021 Monemvassitis

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Ergodicity in bidimensional sphere systems

Athina Monemvassitis A. Guillin, M. Michel, S. Monteil

Laboratoire de Mathématiques Blaise Pascal, Université Clermont Auvergne (France)

Abstract Event-chain Monte Carlo (ECMC) algorithms are fast irreversible Markov-chain Monte Carlo methods. Developed first in hard sphere systems [1], they rely on the breaking of the detailed balance condition to speed up the sampling with respect to their reversible counterparts. However, to insure the sampling of the right target distribution they need the property of ergodicity. I will present a proof of ergodicity (resp. connectivity) for bidimensional soft (resp. hard) sphere systems, casting the ECMC methods in the framework of Piecewise Deterministic Markov Processes [2].

[1] Bernard, Etienne P. and Krauth, Werner and Wilson, David B. "Event-chain Monte Carlo algorithms for hard-sphere systems." Phys. Rev. E, vol. 80, 2009.

[2] Davis, M. H. A. “Piecewise-Deterministic Markov Processes: A General Class of Non-Diffusion Stochastic Models.” Journal of the Royal Statistical Society. Series B (Methodological), vol. 46, no. 3, 1984.

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