Relative Complexity of Random Walks in Random Scenery in the absence of a weak invariance principle for the local times

2015/06/01 by Deligiannidis, George, Kosloff, Zemer
#37A05 #37A35 #60G50 #60K99 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1506.00422

Abstract

We answer the question of Aaronson about the relative complexity of Random Walks in Random Sceneries driven by either aperiodic two dimensional random walks, two-dimensional Simple Random walk, or by aperiodic random walks in the domain of attraction of the Cauchy distribution. A key step is proving that the range of the random walk satisfies the Fölner property almost surely.

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