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

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.

References in corpus (5)

• Geometric integrators and the Hamiltonian Monte Carlo method
• Statistical properties of determinantal point processes in high-dimensional Euclidean spaces
• Dynamics of a planar Coulomb gas
• Polynomial Ensembles and Recurrence Coefficients
• Powers of Ginibre Eigenvalues

Cited by in corpus (10)

• Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems
• Geometric ergodicity of Langevin dynamics with Coulomb interactions
• A localization theorem for the planar Coulomb gas in an external field
• On boundary confinements for the Coulomb gas
• Macroscopic and edge behavior of a planar jellium
• Coulomb gases under constraint: some theoretical and numerical results
• Territorial behaviour of buzzards versus random matrix spacing distributions
• Interactions Between Different Birds of Prey as a Random Point Process
• Fast sampling from $\beta$-ensembles
• Anomalous energy correlations and spectral form factor in the nonergodic phase of the $\beta$-ensemble