## Electronic Journal of Probability

- Electron. J. Probab.
- Volume 22 (2017), paper no. 92, 41 pp.

### Asymptotic direction for random walks in mixing random environments

Enrique Guerra and Alejandro F. Ramírez

#### Abstract

We prove that every random walk in a uniformly elliptic random environment satisfying the cone-mixing condition and a non-effective polynomial ballisticity condition with high enough degree has an asymptotic direction.

#### Article information

**Source**

Electron. J. Probab., Volume 22 (2017), paper no. 92, 41 pp.

**Dates**

Received: 11 November 2016

Accepted: 11 August 2017

First available in Project Euclid: 24 October 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ejp/1508810545

**Digital Object Identifier**

doi:10.1214/17-EJP93

**Mathematical Reviews number (MathSciNet)**

MR3718720

**Zentralblatt MATH identifier**

06797902

**Subjects**

Primary: 60K37: Processes in random environments 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50] 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

**Keywords**

random walk in random environment ballisticity conditions cone-mixing

**Rights**

Creative Commons Attribution 4.0 International License.

#### Citation

Guerra, Enrique; Ramírez, Alejandro F. Asymptotic direction for random walks in mixing random environments. Electron. J. Probab. 22 (2017), paper no. 92, 41 pp. doi:10.1214/17-EJP93. https://projecteuclid.org/euclid.ejp/1508810545