Proof of Aldous' spectral gap conjecture

Опубликовано 17 августа 2016, 21:58

A well known conjecture asserts that on any graph the random walk and the interchange process have the same spectral gap. I will present recent work in collaboration with T.M. Liggett and T. Richthammer, in which we prove the conjecture using a recursive strategy. The main novelty is an idea based on electric network reduction, which allows us to reduce the problem to the proof of a new comparison inequality between certain weighted graphs.