@article{ECP3081,
author = {Ori Gurel-Gurevich and Yuval Peres and Ofer Zeitouni},
title = {Localization for controlled random walks and martingales},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {19},
year = {2014},
keywords = {Controlled random walks; Martingales},
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.},
pages = {no. 24, 1-8},
issn = {1083-589X},
doi = {10.1214/ECP.v19-3081},
url = {http://ecp.ejpecp.org/article/view/3081}}