Localization for controlled random walks and martingales

Ori Gurel-Gurevich, Yuval Peres, Ofer Zeitouni

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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(Sun = 0) decays at polynomial rate n 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.

Original languageAmerican English
JournalElectronic Communications in Probability
StatePublished - 18 Apr 2014


  • Martingale
  • Random walk
  • Stochastic control


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