Mixing Time and Cutoff for One Dimensional Particle Systems

Explore the quantitative aspects of Markov chain convergence in this 46-minute lecture by Hubert Lacoin for the International Mathematical Union. Delve into the study of mixing time for Markov chains, focusing on the cutoff phenomenon—an abrupt convergence to equilibrium. Survey recent results concerning the total-variation mixing time of the simple exclusion process on the segment (both symmetric and asymmetric) and its continuum analog, the simple random walk on the simplex. Gain insights into fundamental results in Markov chain theory, including the convergence of irreducible continuous Markov chains on finite states to unique invariant measures. Access accompanying presentation slides for a comprehensive understanding of this advanced mathematical topic.