 
February 18: Thomas Richthammer (University of
California, Los Angeles)
Title: A proof of Aldous' spectral gap conjecture.
Abstract: Aldous' spectral gap conjecture
asserts that on any finite graph the random walk process and the random
transposition process (which is also known as stirring process or interchange
process) have the same spectral gap. I will give a proof of this conjecture
using a recursive strategy. The approach is a natural extension of the method
already used to prove the validity of the conjecture on trees. The novelty is an
idea based on electric network reduction, which reduces the problem to the proof
of an explicit inequality for a random transposition operator involving both
positive and negative rates. The proof of the latter inequality uses suitable
coset decompositions of the associated matrices on permutations. (Joint work
with Tom Liggett and Pietro Caputo.)
