Limit Profiles of Reversible Markov chains

Abstract: It all began with card shuffling. Diaconis and Shahshahani studied the random transpositions shuffle; pick two cards uniformly at random and swap them. They introduced a Fourier analysis technique to prove that it takes $1/2 n \log n$ steps to shuffle a deck of $n$ cards this way. Recently, Teyssier extended this technique to study the exact shape of the total variation distance of the transition matrix at the cutoff time from the stationary measure, giving rise to the notion of a limit profile. In this talk, I am planning to discuss a joint work with Olesker-Taylor, which extends the above technique from conjugacy invariant random walks to general, reversible Markov chains. I will also present a new technique that allows to study the limit profile of star transpositions, which turns out to have the same limit profile as random transpositions.

mathematical physicsanalysis of PDEsclassical analysis and ODEscombinatoricscomplex variablesfunctional analysisinformation theorymetric geometryoptimization and controlprobability

Audience: researchers in the topic

Probability and Analysis Webinar

Series comments: Subscribe to our seminar for weekly announcements at sites.google.com/view/paw-seminar/subscribe Follow us on twitter twitter.com/PAW_seminar

Subscribe to our youtube channel to watch recorded talks www.youtube.com/channel/UCO7mXgeoAFYG2Q17XDRQobA