Thumbnail

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

Chafaï, Djalil; Ferré, Gregoire (2019), Simulating Coulomb gases and log-gases with hybrid Monte Carlo algorithms, Journal of Statistical Physics, 174, p. 692–714. 10.1007/s10955-018-2195-6

View/Open
Type
Article accepté pour publication ou publié
Date
2019
Journal name
Journal of Statistical Physics
Volume
174
Publisher
Springer
Pages
692–714
Publication identifier
Metadata
Show full item record
Author(s)
Chafaï, Djalil cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Ferré, Gregoire
Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
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.
Subjects / Keywords
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