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Simulating Coulomb gases and log-gases with hybrid Monte Carlo algorithms

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1806.05985.pdf (607.9Kb)
Date
2019
Dewey
Probabilités et mathématiques appliquées
Sujet
Numerical Simulation; Random number generator; Singular Stochastic Differential Equation; Coulomb gas; Monte Carlo Adjusted Langevin; Hybrid Monte Carlo; Markov Chain Monte Carlo; Langevin dynamics; Kinetic equation
Journal issue
Journal of Statistical Physics
Volume
174
Publication date
2019
Article pages
692–714
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s10955-018-2195-6
URI
https://basepub.dauphine.fr/handle/123456789/17956
Collections
  • CEREMADE : Publications
Metadata
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Author
Chafaï, Djalil
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Ferré, Gregoire
51621 Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
Type
Article accepté pour publication ou publié
Abstract (EN)
Coulomb and log-gases are exchangeable singular Boltzmann-Gibbs measures appearing in mathematical physics at many places, in particular in random matrix theory. We explore experimentally an efficient numerical method for simulating such gases. It is an instance of the Hybrid or Hamiltonian Monte Carlo algorithm, in other words a Metropolis-Hastings algorithm with proposals produced by a kinetic or underdamped Langevin dynamics. This algorithm has excellent numerical behavior despite the singular interaction, in particular when the number of particles gets large. It is more efficient than the well known overdamped version previously used for such problems.

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