This talk covered the portion of my Ph.D. thesis results concerning the multicolour East model (and the associated paper). Slides can be found here.

Abstract

We consider the multicolour East model, a new model in the mathematics literature that is best described as multiple multidimensional East models sharing the neutral state. Looking at the simplest version, the two-colour East model in two dimensions we show ergodicity and analyse sufficient conditions to get asymptotics on the spectral gap in the limit of vanishing transition rates of one of the two colours. We close the talk by looking at generalisations of these results and remaining open questions.