Philip Matchett Wood: Random doubly stochastic tridiagonal matrices

Abstract

Let T_n be the set doubly stochastic tridiagonal matrices. Such a matrix defines a birth and death chain, and it is natural to ask about the properties of a `typical' birth and death chain by sampling uniformly at random from T_n. This talk will discuss how to pick an element T of T_n uniformly at random, revealing a connection with random sampling of alternating (up-down) permutations. With a typical element T in hand, we will ask many questions---and answer some of them, too---including studying the distribution of the entries, the eigenvalues, and mixing times. This is joint work with Persi Diaconis.