Conference ID: 939-3301-2582
PIN Code: 326882
In this talk I will present some recent results on mean field limits for interacting diffusions. We will study, in particular, problems for which the mean field limit exhibits phase transitions, in the sense that the limiting McKean-Vlasov PDE can have more than one stationary states, at sufficiently strong interaction strengths. We provide a general characterization of first and second order phase transitions for mean field dynamics on the torus and we study fluctuations around the mean field limit. As a case study, we consider the combined mean field/homogenization limit for noisy Kuramoto oscillators. Applications of this type of dynamics to models for opinion formation and to sampling and optimization algorithms are also discussed.
G.A. Pavliotis is professor of Applied Mathematics and Head of the Applied Mathematics and Mathematical Physics section at the department of mathematics, Imperial College London where he has been since 2004. Prior to this, he held a postdoctoral position at the Mathematics Institute, Warwick University. He obtained his PhD from Rensselear Polytechnic Institute in May 2002. He has held visiting professorships at Ecole des Ponts, Paris, France, FU Berlin, Germany, TU Munich, Germany and EPFL, Switzerland. His main research interests are the development of sampling and optimization algorithms, non-equilibrium statistical mechanics and the development of analytical and computational methods for stochastic systems with stochastic effects.