Quenched invariance principle for random walks in balanced random environment
By Xiaoqin Guo, Ofer Zeitouni. Probability theory and related fields, 2010
61 citations recorded by the source corpus.
We consider random walks in a balanced random environment in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Z}^d}$$\end{document}, d ≥ 2. We first prove an invariance principle (for d ≥ 2) and the transience of the random walks when d ≥ 3 (recurrence when d = 2) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for random walks in i.i.d. balanced environments.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f446a5be3bf6c5ffa31b55c57c8cc6241e427d88
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Invariance principle for the random conductance model in a degenerate ergodic environment (2013, background): “environments under some moment conditions [27], whereas in the i.”
- Recent progress on the Random Conductance Model (2011, background): “(1.37) This situation can be analyzed with the help of standard methods of largedeviation theory (cf, e.g., Dembo and Zeitouni [45], den Hollander [79]) — in fact, Cramér’s theorem more or less suffices — and so one can prove: Exercise 1.20.”