## Electronic Journal of Probability

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

#### 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
Accepted: 13 September 2017
First available in Project Euclid: 9 October 2017

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

#### 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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