Spectrum of Random-to-Random Shuffling in the Hecke Algebra

Explore the intriguing world of random-to-random shuffling in this 21-minute conference talk presented by Sarah Brauner from the University of Quebec Montréal. Delve into the elegant formulas behind the eigenvalues of this Markov chain and discover how they relate to mixing time. Learn about the recent resolution of a 20-year-old conjecture regarding non-negative integer eigenvalues. Examine the generalization of random-to-random shuffling to the Type A Hecke algebra, uncovering combinatorial expressions for eigenvalues as polynomials with non-negative integer coefficients. Gain insights into the simplified proof methods that connect random-to-random shuffling with Jucys-Murphy elements of the Hecke algebra. Recorded at IPAM's Integrability and Algebraic Combinatorics Workshop, this talk offers a fascinating glimpse into cutting-edge research in algebraic combinatorics and Markov chain theory.