I will discuss a system of interacting particles subject to two competing effects: a pairwise repulsive interaction and an external confining potential. At positive temperature, the system is described by a Gibbs measure, and the central question is to understand its behavior as the number of particles tends to infinity. In the high-temperature regime, one expects the entropy to dominate the interaction at microscopic scales, leading to Poissonian local statistics. Despite this natural expectation, Poisson convergence has so far been established only in rather specific settings, and typically under very strong assumptions on the growth of the temperature.

In this talk, I will present new regimes in which Poisson convergence holds, and explain the main ideas behind the proof.
No background in statistical physics is needed.