The interchange process on high-dimensional products

We resolve a long-standing conjecture of Wilson (Ann. Appl. Probab. 14 (2004) 274–325), reiterated by Oliveira (2016), asserting that the mixing time interchange process with unit edge rates on n-dimensional hypercube is order n. This follows from sharp inequality established at level Dirichlet forms, which we also deduce macroscopic cycles emerge in constant time, and log-Sobolev exclusion 1. Beyond hypercube, our results apply to cartesian products arbitrary graphs fixed size, shedding light broad 41 (2013) 871–913).