Simulating Coulomb gases and log-gases with hybrid Monte Carlo algorithms
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Publication:6303064
DOI10.1007/S10955-018-2195-6arXiv1806.05985WikidataQ128901558 ScholiaQ128901558MaRDI QIDQ6303064
Publication date: 15 June 2018
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.
Monte Carlo methods (65C05) Interacting particle systems in time-dependent statistical mechanics (82C22) Random measures (60G57)
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