Prof. Filippo Cesi
Universita' La Sapienza Roma

Titolo: THE ALDOUS' SPECTRAL GAP PHENOMENON

Mercoledi' 14 Novembre 2018 ORE 16:00

Dipartimento di Matematica e Fisica
Universita' degli Studi Roma Tre
Largo San Leonardo Murialdo, 1 - Pal.C - Aula 211

Abstract:
Some families of Markov chains have a spectral gap which coincides
with the spectral gap of an extremely simplified version of the chain.
Another way of restating the same concept is: some families of Cayley
graphs have a spectral gap which can be found in a very low
dimensional representation of the underlying group. We will present a
general approach which could be useful when going fishing for this
phenomenon in an arbitrary finite group. Two specific examples will be
discussed: the case of the symmetric group which corresponds to the
"original" Aldous' spectral gap conjecture, proven in 2010 by Caputo,
Liggett and Richthammer, and case of the Weyl group W(B_n) we studied
in a recent paper.