## Electronic Communications in Probability

- Electron. Commun. Probab.
- Volume 7 (2002), paper no. 19, 191-197.

### A Non-Ballistic Law of Large Numbers for Random Walks in I.I.D. Random Environment

#### Abstract

We prove that random walks in i.i.d. random environments which oscillate in a given direction have velocity zero with respect to that direction. This complements existing results thus giving a general law of large numbers under the only assumption of a certain zero-one law, which is known to hold if the dimension is two.

#### Article information

**Source**

Electron. Commun. Probab., Volume 7 (2002), paper no. 19, 191-197.

**Dates**

Accepted: 30 September 2002

First available in Project Euclid: 16 May 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.ecp/1463434786

**Digital Object Identifier**

doi:10.1214/ECP.v7-1060

**Mathematical Reviews number (MathSciNet)**

MR1937904

**Zentralblatt MATH identifier**

1008.60107

**Subjects**

Primary: 60K37: Processes in random environments

Secondary: 60F15: Strong theorems

**Keywords**

Random walk in random environment RWRE law of large numbers

**Rights**

This work is licensed under aCreative Commons Attribution 3.0 License.

#### Citation

Zerner, Martin. A Non-Ballistic Law of Large Numbers for Random Walks in I.I.D. Random Environment. Electron. Commun. Probab. 7 (2002), paper no. 19, 191--197. doi:10.1214/ECP.v7-1060. https://projecteuclid.org/euclid.ecp/1463434786