Electronic Journal of Probability

Conditions for ballisticity and invariance principle for random walk in non-elliptic random environment

Mark Holmes and Thomas S. Salisbury

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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.

Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 81, 18 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1507536148

Digital Object Identifier
doi:10.1214/17-EJP107

Mathematical Reviews number (MathSciNet)
MR3710801

Zentralblatt MATH identifier
06797891

Subjects
Primary: 60K37: Processes in random environments

Keywords
random walk non-elliptic random environment zero-one law ballisticity invariance principle

Rights
Creative Commons Attribution 4.0 International License.

Citation

Holmes, Mark; Salisbury, Thomas S. Conditions for ballisticity and invariance principle for random walk in non-elliptic random environment. Electron. J. Probab. 22 (2017), paper no. 81, 18 pp. doi:10.1214/17-EJP107. https://projecteuclid.org/euclid.ejp/1507536148


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