Poisson-Dirichlet Distribution for the Interchange Process in Five Dimensions

Explore the emergence of macroscopic cycles in the interchange process on high-dimensional tori through this 47-minute lecture presented by Dor Elboim from the Institute for Advanced Study. Delve into the study of random permutations formed by particle interchanges on graph vertices, focusing on the cycle structure and the appearance of long cycles. Examine the process on tori with dimensions greater than or equal to 4, and discover how macroscopic cycles emerge after extended time periods. Learn about the convergence of cycle lengths to the Poisson-Dirichlet distribution and gain insights from this joint work with Allan Sly, presented at IPAM's Statistical Mechanics Beyond 2D Workshop.