Localization for controlled random walks and martingales
Probability
2013-09-19 v1
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.
Cite
@article{arxiv.1309.4512,
title = {Localization for controlled random walks and martingales},
author = {Ori Gurel-Gurevich and Yuval Peres and Ofer Zeitouni},
journal= {arXiv preprint arXiv:1309.4512},
year = {2013}
}