Abstract
Hyperuniformity is the property of collections of random points for which the variance of the number of points in a large box is negligible compared to the volume of the box. This notion, introduced by S. Torquato (a theoretical chemist) in the early 2000s as a way of characterizing systems " disordered but more rigid than Poisson " has enjoyed real success at the interface between physics and probability. In this talk, we focus on a statistical physics model : Coulomb gas in dimension 2, also known as log-gas, or " plasma with one component ". A series of physics papers from the years 1980-1990 predicted a phenomenon " cancellation of charge fluctuations " equivalent to hyperuniformity. I will present a proof of this, as well as the distance separating us from the full scope of these predictions.
