Cutoff for the bidirectional East Process

2020/09/12 by Lyubarskaja, Anna
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2009.05832

Abstract

This paper will examine the cutoff for a random process on the hypercube, \0, 1\^L, closely related to the East Process. In this process, every coordinate has two 1/2-Poisson clocks at each coordinate which add the coordinate to the previous or next one when they ring. We show that the cutoff is L/v with a window of order √(L), where v is the speed of the front. We compare these results to the cutoff for the East Process and the cutoff for a non-local version of this same process studied by Ganguly, Lubetzky, and Martinelli as well as Ben-Hamou and Peres.

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