Seminari del Dipartimento
Probabilita' THE ALDOUS' SPECTRAL GAP PHENOMENON Filippo Cesi 14-11-2018 - 16:00 Largo San Leonardo Murialdo,1 - Pal.C - Aula 211
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. |