# Mathematics Colloquia and Seminars

Let $T_n$ be the compact convex set of tridiagonal doubly stochastic matrices. Â These arise naturally as birth and death chains with a uniform stationary distribution. Â One can think of a âtypicalâ matrix $T_n$ as one chosen uniformly at random, and this talk will present a simple algorithm to sample uniformly in $T_n$. Â Once we have our hands on a 'typical' element of $T_n$, there are many natural questions to ask: Â What are the eigenvalues? What is the mixing time? Â What is the distribution of the entries? Â This talk will explore these and other questions, with a focus on whether a random element of $T_n$ exhibits a cutoff in its approach to stationarity. Â Joint work with Persi Diaconis.