Appears in collection : 2025 IHES Summer School – Statistical Aspects of Nonlinear Physics

In this course, I'll first discuss briefly the equilibrium systems with long-range correlations (such as the log-gas or the Riesz gas in coordination with the course by S. Serfaty). Then the main emphasis of my course would be on nonequilibrium stationary states of many-body systems with attractive long-range correlations. I will provide examples of how such states can be generated by stochastic resetting of N diffusing particles in one or higher dimensions. The joint distribution of the positions of the particles, though not factorizable due to strong correlations, has a certain conditionally independent structure that allows them to be exactly solvable for various physical obsevables. For example, in one dimension and in the large N limit, one can compute exactly, the average density, the extreme value statistics, the spacing distribution between particles as well as the full counting statistics. The presence of long-range correlations make these observables drastically different from the equilibrium ideal gas where the joint distribution in the stationary state factorizes.