Michał Kotowski: Macroscopic cycles in the interchange process and the quantum Heisenberg model on the Hamming graph

Speaker:  Michał Kotowski

Title: Macroscopic cycles in the interchange process and the quantum Heisenberg model on the Hamming graph

Abstract: The topic of this talk will be random permutations coming from the interchange process and its generalizaton, the quantum Heisenberg model from statistical physics, on the 2-dimensional Hamming graph. We prove the existence of a phase transition - in the interchange process for sufficiently long times there exists, with high probability, a cycle of macroscopic size, while for short times all cycles are small. This is the first result of this kind for a graph with nontrivial geometry, generalizing known results due to Schramm (2008). One of the main techniques used is the cyclic time random walk. Joint work with Radosław Adamczak and Piotr Miłoś.