Excited random walks with non-nearest neighbor steps

2015/04/20 by Davis, Burgess, Peterson, Jonathon
#60J15 #60K35 #60K37 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1504.05124

Abstract

Let W be an integer valued random variable satisfying E[W] =: δ≥ 0 and P(W<0)>0, and consider a self-interacting random walk that behaves like a simple symmetric random walk with the exception that on the first visit to any integer x∈ ℤ the size of the next step is an independent random variable with the same distribution as W. We show that this self-interacting random walk is recurrent if δ≤ 1 and transient if δ>1. This is a special case of our main result which concerns the recurrence and transience of excited random walks (or cookie random walks) with non-nearest neighbor jumps.

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