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- Title
Simulating Coulomb and Log-Gases with Hybrid Monte Carlo Algorithms.
- Authors
Chafaï, Djalil; Ferré, Grégoire
- Abstract
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, and allows new numerical explorations. It suggests for instance to conjecture a universality of the Gumbel fluctuation at the edge of beta Ginibre ensembles for all beta.
- Subjects
COULOMB functions; BOLTZMANN-Gibbs distribution (Statistical physics); MONTE Carlo method; ALGORITHMS; LANGEVIN equations; NUMERICAL analysis
- Publication
Journal of Statistical Physics, 2019, Vol 174, Issue 3, p692
- ISSN
0022-4715
- Publication type
Article
- DOI
10.1007/s10955-018-2195-6