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Philip Matchett Wood : Random doubly stochastic tridiagonal matrices (Dec 1, 2011 4:10 PM)

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 ‘typical’ 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.

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