Persi Diaconis

Random Tri-Diagonal Doubly Stochastic Matrices

ABSTRACT The set of n x n tri-diagonal, doubly stochastic
matrices is a compact, convex set (birth and death chains with
a uniform stationary distribution). Thus, it inherits a natural
uniform distribution. Pick such a matrix at random, how are its
eigenvalues, mixing times, and entries distributed? The answers
involve nice combinatorics (alternating permutations),
orthogonal polynomials, and some non-standard limit theory.
This is joint work with Phillip Wood.

BIO: Persi Diaconis has done pioneering work on mixing rates of
Markov chains, and his numerous results in this area have had a
huge impact. He has also made fundamental contributions to
other areas of probability and combinatorics and to Statistics.
He is a member of the National Academy of Sciences, a MacArthur
fellow, and is particularly famous for his engaging lectures.