UVictoria Probability and Dynamics Seminar: Lucas Teyssier

We will discuss extensions of random transpositions to other conjugacy classes. Our main probabilistic result is the total variation cutoff profile for these random walks, under a mild assumption on the number of fixed points. The proof is based on a new method to estimate the characters of symmetric groups, that makes use of exicited diagrams. During the talk we will present the main combinatorial formulas that allow to compute the eigenvalues of such chains, and give ideas on how to estimate them asymptotically. Based on joint work with Sam Olesker-Taylor and Paul Thévenin.