Kodai Mathematical Journal

Large deviations for simple random walk on supercritical percolation clusters

Naoki Kubota

Full-text: Open access

Abstract

We prove quenched large deviation principles governing the position of the random walk on a supercritical site percolation on the integer lattice. A feature of this model is non-ellipticity of transition probabilities. Our analysis is based on the consideration of so-called Lyapunov exponents for the Laplace transform of the first passage time. The rate function is given by the Legendre transform of the Lyapunov exponents.

Article information

Source
Kodai Math. J., Volume 35, Number 3 (2012), 560-575.

Dates
First available in Project Euclid: 15 November 2012

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1352985454

Digital Object Identifier
doi:10.2996/kmj/1352985454

Mathematical Reviews number (MathSciNet)
MR2997480

Zentralblatt MATH identifier
1261.60098

Citation

Kubota, Naoki. Large deviations for simple random walk on supercritical percolation clusters. Kodai Math. J. 35 (2012), no. 3, 560--575. doi:10.2996/kmj/1352985454. https://projecteuclid.org/euclid.kmj/1352985454


Export citation