A quenched invariance principle for certain ballistic random walks in i.i.d. environments

2007/02/11 by Noam Berger, Berger, Noam, Ofer Zeitouni +1 · 1 citation
Mathematics · #Stochastic processes and statistical mechanics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/0702306

Abstract

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.

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