Localization for controlled random walks and martingales

2013/09/18 by Gurel-Gurevich, Ori, Peres, Yuval, Zeitouni, Ofer · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1309.4512

Abstract

We consider controlled random walks that are martingales with uniformly bounded increments and nontrivial jump probabilities and show that such walks can be constructed so that P(S_n^u=0) decays at polynomial rate n^-α where α>0 can be arbitrarily small. We also show, by means of a general delocalization lemma for martingales, which is of independent interest, that slower than polynomial decay is not possible.

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