5 problems

Aldous–Diaconis conjecture. In this regime, the random walk exhibits cutoff with high probability.

Let $f$ satisfy the hypotheses above, with $f”(L/2-h)=-C\lvert h\rvert^{\alpha}+o(\lvert h\rvert^{\alpha})$ for $\alpha>0$, and let $\tau_n$ denote the separation time of the Brown…

Let the Swendsen–Wang dynamics be defined on a lattice graph, with temperature allowed to vary and with criticality referring to the model's critical temperature. Lattice cutoff co…

Let $S_n$ be the symmetric group, and consider the family of walks referred to in the source for a generating set formed from a transposition and an $n$-cycle, together with one ad…

Let $\tau_{s(n)}$ denote the mixing-time scale and let $\lambda_{s(n)}$ denote the relevant eigenvalue for the Metropolis chain, with the associated random birth and death chain as…