Systems with Coulomb Interactions: Mean-Field Limits and Statistical Mechanics - Lecture 1

Explore the intricacies of large systems of particles with Coulomb-type repulsion in this comprehensive lecture by Sylvia Serfaty from the Courant Institute. Delve into two main parts: first, examine the question of mean-field for the dynamics of these systems using a modulated energy approach. Then, dive deeper into the statistical mechanics of Coulomb systems, covering topics such as free energy expansion, Large Deviation Principle (LDP) for empirical fields, and fluctuations around the mean-field limit. Discover the common tools and ideas that bridge both parts of this nearly two-hour presentation, offering a thorough understanding of Coulomb interactions in particle systems.