## Electronic Journal of Probability

### Random walks with unbounded jumps among random conductances I: Uniform quenched CLT

#### Abstract

We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails of the jumps) we prove a quenched uniform invariance principle for the random walk. This means that the rescaled trajectory of length n is (in a certain sense) close enough to the Brownian motion, uniformly with respect to the choice of the starting location in an interval  of length $O(\sqrt{n})$ around the origin.

#### Article information

Source
Electron. J. Probab., Volume 17 (2012), paper no. 85, 22 pp.

Dates
Accepted: 4 October 2012
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465062407

Digital Object Identifier
doi:10.1214/EJP.v17-1826

Mathematical Reviews number (MathSciNet)
MR2988400

Zentralblatt MATH identifier
1252.60100

Rights

#### Citation

Gallesco, Christophe; Popov, Serguei. Random walks with unbounded jumps among random conductances I: Uniform quenched CLT. Electron. J. Probab. 17 (2012), paper no. 85, 22 pp. doi:10.1214/EJP.v17-1826. https://projecteuclid.org/euclid.ejp/1465062407

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