Localization for controlled random walks and martingales

Ori Gurel-Gurevich (None)
Yuval Peres (Microsoft Research)
Ofer Zeitouni (Weizmann Institute)


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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Pages: 1-8

Publication Date: April 26, 2014

DOI: 10.1214/ECP.v19-3081


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