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(Random) Tri-Diagonal, Doubly Stochastic Matrices, Orthogonal Polynomials and Alternating Permutations
September 16, 2010 (11:30 AM PDT - 12:10 PM PDT)
Persi Diaconis (Stanford University)
The set of tri-diagonal, doubly stochastic matrices is a compact convex set. Thus, it makes sense to "pick such a matrix uniformly" and ask about its properties (spectral gap, mixing times, minimum entry, ...). This is intimately connected with the combinatorics of alternating matrices. Jacoby polynomials make a serious appearance. All of this is joint work with Philip Matchett Wood.
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