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Explore the statistical mechanics of large particle systems with Coulomb or Riesz long-range repulsion through an electrostatic formulation approach in this comprehensive lecture by Sylvia Serfaty from Sorbonne Université and the Courant Institute of Mathematical Sciences. Delve into fundamental concepts including equilibrium measures and their properties, examine the expansion of free energy in these complex systems, and analyze limit point processes that emerge from large-scale particle interactions. Investigate the nature of fluctuations in systems with long-range repulsive forces and understand how electrostatic methods provide powerful tools for analyzing these mathematical physics problems. Gain insights into advanced techniques used to study many-body systems where particles interact through inverse power law potentials, building essential knowledge for research in mathematical physics, probability theory, and statistical mechanics.
