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arXiv · 1309.4512

Localization for controlled random walks and martingales

Ori Gurel-Gurevich·Yuval Peres·Ofer Zeitouni
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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^{-\alpha} where \alpha>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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Ori Gurel-Gurevich, Yuval Peres, Ofer Zeitouni. 2013-09-18. Localization for controlled random walks and martingales. https://arxiv.org/abs/1309.4512

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