Cutoff for the Symmetric Exclusion Process in dimensions d ≥ 2

Establish total-variation cutoff for the m-particle Symmetric Exclusion Process on growing lattices or tori in spatial dimensions d ≥ 2.

Background

The occurrence of cutoff for exclusion dynamics has been rigorously proved in one dimension (segments/cycles) using strong monotonicity, but this approach breaks down in higher dimensions. Wilson conjectured cutoff on various graph sequences with detailed predictions for location, width, and profile, which remain unproved in higher-dimensional lattices or tori.