From Poisson particles to Gibbs swarms: large deviations and MCMC

Abstract

We study moving particles whose collective configurations are modelled by a Gibbs transformation of a dilute Poisson reference system. A large-deviation principle identifies the competition between entropy and interaction energy, yields the limiting free energy, and characterizes the typical configurations under the Gibbs law. For Brownian particles, this representation leads naturally to Metropolis--Hastings algorithms on trajectories and relative positions. We illustrate the framework using experimental data on magnetically driven micromotors and their chain formation.