Michał Kotowski (University of Warsaw): Macroscopic cycles in the interchange process and the quantum Heisenberg model on the Hamming graph

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.