Nonequilibrium Point Processes with Long-range Correlations - 2/3

Explore nonequilibrium stationary states of many-body systems with attractive long-range correlations in this advanced physics lecture. Begin with a brief overview of equilibrium systems featuring long-range correlations, including log-gas and Riesz gas models, before diving deep into the main focus on nonequilibrium scenarios. Discover how stochastic resetting of N diffusing particles in one or higher dimensions generates these complex states, and learn about the conditionally independent structure of joint particle position distributions that enables exact analytical solutions despite strong correlations preventing factorization. Master the computation of key physical observables in the large N limit for one-dimensional systems, including average density calculations, extreme value statistics, particle spacing distributions, and full counting statistics. Understand how long-range correlations fundamentally alter these observables compared to equilibrium ideal gas systems where joint distributions factorize in stationary states, revealing the dramatic differences between equilibrium and nonequilibrium many-body physics.