Translator Disclaimer
2017 Conditions for ballisticity and invariance principle for random walk in non-elliptic random environment
Mark Holmes, Thomas S. Salisbury
Electron. J. Probab. 22: 1-18 (2017). DOI: 10.1214/17-EJP107

Abstract

We study the asymptotic behaviour of random walks in i.i.d. non-elliptic random environments on $\mathbb{Z} ^d$. Standard conditions for ballisticity and the central limit theorem require ellipticity, and are typically non-local. We use oriented percolation and martingale arguments to find non-trivial local conditions for ballisticity and an annealed invariance principle in the non-elliptic setting. The use of percolation allows certain non-elliptic models to be treated even though ballisticity has not been proved for elliptic perturbations of these models.

Citation

Download Citation

Mark Holmes. Thomas S. Salisbury. "Conditions for ballisticity and invariance principle for random walk in non-elliptic random environment." Electron. J. Probab. 22 1 - 18, 2017. https://doi.org/10.1214/17-EJP107

Information

Received: 18 March 2017; Accepted: 13 September 2017; Published: 2017
First available in Project Euclid: 9 October 2017

zbMATH: 06797891
MathSciNet: MR3710801
Digital Object Identifier: 10.1214/17-EJP107

Subjects:
Primary: 60K37

JOURNAL ARTICLE
18 PAGES


SHARE
Vol.22 • 2017
Back to Top