Cutoff conjecture for simple random walk on vertex-transitive expander graphs

Let $(G_n)$ be any family of finite vertex-transitive expander graphs, and let the simple random walk (SRW) be the walk that at each step moves uniformly to a neighboring vertex. Vertex-transitive expander cutoff conjecture. The SRW on any family of vertex-transitive expander graphs exhibits cutoff. The paper has established cutoff for simple and non-backtracking random walks on almost every $d$-regular graph in its stated degree range, but notes that arbitrary expander families may have asymmetric counterexamples and presents this assertion as plausible; its general validity remains open.