Electronic Journal of Probability

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

Christophe Gallesco and Serguei Popov

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60K37: Processes in random environments

ergodic environment unbounded jumps hitting probabilities exit distribution

This work is licensed under aCreative Commons Attribution 3.0 License.


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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