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Explore nonequilibrium point processes with long-range correlations in this comprehensive lecture delivered by Satya N. Majumdar from LPTMS at the Institut des Hautes Etudes Scientifiques. Begin with a brief examination of equilibrium systems exhibiting long-range correlations, including log-gas and Riesz gas systems, before diving deep into the main focus on nonequilibrium stationary states of many-body systems with attractive long-range correlations. Discover how such states emerge through stochastic resetting of N diffusing particles in one and higher dimensions, and learn about the unique conditionally independent structure of joint particle position distributions that enables exact solvability 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, spacing distribution between particles, and full counting statistics. Understand how the presence of long-range correlations fundamentally alters these observables compared to equilibrium ideal gas systems where joint distributions factorize in stationary states, providing crucial insights into the behavior of complex many-body systems far from equilibrium.
