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Titre: Spectrum of random-to-random shuffling in the Hecke algebra

搁茅蝉耻尘茅: The eigenvalues of a Markov chain determine its mixing time. In this talk, I will describe a Markov chain on the symmetric group called random-to-random shuffling whose eigenvalues have surprisingly elegant鈥攖hough mysterious鈥攆ormulas. In particular, these eigenvalues were shown to be non-negative integers by Dieker and Saliola in 2017, resolving an almost 20 year conjecture.

In recent work with Ilani Axelrod-Freed, Judy Chiang, Patricia Commins and Veronica Lang, we generalize random-to-random shuffling to a Markov chain on the Type A Iwahori Hecke algebra, and prove combinatorial expressions for its eigenvalues as a polynomial in q with non-negative integer coefficients. Our methods simplify the existing proof for q=1 by drawing novel connections between random-to-random shuffling and the Jucys-Murphy elements of the Hecke algebra.

Location: Local: PK-4323