Recent Progress on Mean-Field Dynamics of Coulomb/Riesz Gases

Explore the mathematical foundations of mean-field dynamics in this conference talk examining the convergence behavior of Coulomb and Riesz gases through the lens of entropy, energy, and functional inequalities. Delve into the rigorous analysis of how interacting particle systems achieve mean-field convergence and propagation of chaos, with particular emphasis on the mathematical techniques used to establish these fundamental results. Discover the critical role that trend to equilibrium plays in the mean-field equation and how this property enables the derivation of uniform-in-time convergence results and the establishment of chaos generation. Learn about cutting-edge research on fluctuations around the mean-field limit and gain insights into the sophisticated mathematical tools required to analyze these complex stochastic systems. The presentation covers advanced topics in probability theory, partial differential equations, and statistical mechanics, making it valuable for researchers working in mathematical physics, stochastic analysis, and electrochemical modeling applications.