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Proof of Aldous' spectral gap conjecture

Speaker  Pietro Caputo

Affiliation  Universita Roma Tre

Host  Yuval Peres

Duration  00:46:04

Date recorded  30 August 2010

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.

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> Proof of Aldous' spectral gap conjecture