Analysis of exclusion processes on high-dimensional geometries

Investigate the behavior of the Exclusion Process on high-dimensional geometries, specifically expanders and the Boolean hypercube, which are not covered by the methods developed in the paper.

Background

The paper proves cutoff for the Exclusion Process under a return-probability condition that applies to discrete tori and broad classes of vertex-transitive graphs of moderate growth. The authors explicitly note that their methods do not extend to certain high-dimensional geometries, including expander graphs and the Boolean hypercube. Determining the relevant behavior of the Exclusion Process in these settings is left unresolved.