Title: Transience for the interchange process in dimension 5

Abstract: The interchange process $\sigma_T$ is a random permutation valued 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. In dimension $d \geq 3$ infinite cycles are expected when $T$ is large. The cycles can be interpreted as a random walk which interacts with its past and we give a multi-scale proof establishing transience of the walk (and hence infinite cycles) when $d\geq 5$. 

*Joint work with Dor Elbiom