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Random tridiagonal doubly stochastic matrices

Mathematical Physics & Probability

Speaker: Philip Matchett Wood, Stanford
Location: 1147 MSB
Start time: Wed, Jan 12 2011, 4:10PM

Let $T_n$ be the compact convex set of tridiagonal doubly stochastic matrices.  These arise naturally as birth and death chains with a uniform stationary distribution.  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 $T_n$.  Once we have our hands on a 'typical' element of $T_n$, there are many natural questions to ask:  What are the eigenvalues? What is the mixing time?  What is the distribution of the entries?  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.  Joint work with Persi Diaconis.