Levin–Peres conjecture on cutoff for vertex-transitive expanders

Let $(G_n)_{n\ge 1}$ be a sequence of finite vertex-transitive expander graphs, and consider simple random walk on each $G_n$. Levin–Peres conjecture. The sequence $(G_n)_{n\ge 1}$ exhibits cutoff. This conjecture concerns the long-standing problem of determining when expander sequences exhibit cutoff; it was explicitly raised by D. Levin and Y. Peres, and remains open in general.