The product condition implies cutoff
In the community of mixing times, a famously wrong conjecture asserts that a sequence of ergodic Markov chains exhibits cutoff as soon as the product of their Poincare constant and mixing time tends to infinity. In this talk, I will prove that this conjecture is actually valid, provided one replaces the Poincare constant with its natural non-equilibrium version. This is based on a (very recent) joint work with Francesco Pedrotti.