Week 14.07.2025 – 20.07.2025
Monday (14 Jul)
Amir Abbas Khanbeigi (University of Manchester)
14 Jul at 12:30 - 13:30
KCL, Strand - S5.20
Posted by matteo.tanzi@kcl.ac.uk
Allan Sly (Princeton University)
14 Jul at 15:00 - 16:00
KCL, Strand - K-1.56
The interchange process \sigma_T is a random permutation valued stochastic process on a graph evolving in time by transpositions on its edges at rate 1. On Z^d, when T is small all the cycles of the permutation \sigma_T are finite almost surely but it is conjectured that infinite cycles appear in dimensions 3 and higher for large times. In this talk I will focus on the finite volume case where we establish that macroscopic cycles with Poisson-Dirichlet statistics appear for large times in dimensions 5 and above.
Posted by samuel.g.johnston@kcl.ac.uk