Nonequilibrium Point Processes with Long-range Correlations - Part 1

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 discussion of equilibrium systems exhibiting long-range correlations, including log-gas and Riesz gas systems, before diving into the main focus on nonequilibrium stationary states of many-body systems with attractive long-range correlations. Discover how such states can be generated through stochastic resetting of N diffusing particles in one or higher dimensions, and learn about the conditionally independent structure of joint particle position distributions that enables exact solvability for various physical observables despite strong correlations preventing factorization. Examine detailed calculations for the large N limit in one dimension, including exact computations of average density, extreme value statistics, spacing distribution between particles, and full counting statistics. Understand how the presence of long-range correlations creates dramatically different observables compared to equilibrium ideal gas systems where joint distributions factorize in stationary states, providing crucial insights into the fundamental differences between equilibrium and nonequilibrium statistical mechanics.