  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.
