Department of Mathematics

Indian Institute of Science

Bangalore 560 012






Rajesh Sundaresan 
Affiliation : IISc, Bangalore

Subject Area






Department of Mathematics, Lecture Hall I




03.30 p.m.




September 19, 2016 (Monday)



"A local Lyapunov function for the McKean-Vlasov dynamics."


The McKean-Vlasov dynamics is a large system limit of the evolution of empirical measures of a weakly interacting system of particles. The empirical measure creates a field which then influences the evolution of any single particle. The process of empirical measures is itself a Markov process which has relative entropy with respect to the invariant measure as a natural Lyapunov function. By scaling this Lyapunov function and taking the infinite particle limit, we propose to arrive at a local Lyapunov function for the McKean-Vlasov dynamics. The approach is conceptually simpler than a prior approach, naturally identifies the desired Lyapunov function, and clarifies why the Freidlin-Wentzell quasipotential associated with the interacting system is a local Lyapunov function. (The talk is based on ongoing work with Laurent Miclo.)