A Quenched Invariance Principle for Certain Ballistic Random Walks in i.i.d. Environments

By Noam Berger, Ofer Zeitouni. 2007

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We prove that every random walk in i.i.d. environment in dimension greater than or equal to 2 that has an almost sure positive speed in a certain direction, an annealed invariance principle and some mild integrability condition for regeneration times also satisfies a quenched invariance principle. The argument is based on intersection estimates and a theorem of Bolthausen and Sznitman.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0678de723e116d12d7babe854f37f66907807828