Electronic Communications in Probability

Large deviations for the local times of a random walk among random conductances

Wolfgang König, Michele Salvi, and Tilman Wolff

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We derive an annealed large deviation principle for the normalised local times of a continuous-time random walk among random conductances in a finite domain in $\mathbb{Z}^d$ in the spirit of Donsker-Varadhan [DV75-83]. We work in the interesting case that the conductances may assume arbitrarily small values. Thus, the underlying picture of the principle is a joint strategy of small values of the conductances and large holding times of the walk. The speed and the rate function of our principle are explicit in terms of the lower tails of the conductance distribution. As an application, we identify the logarithmic asymptotics of the lower tails of the principal eigenvalue of the randomized negative Laplace operator in the domain.

Article information

Electron. Commun. Probab., Volume 17 (2012), paper no. 10, 11 pp.

Accepted: 18 February 2012
First available in Project Euclid: 7 June 2016

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Zentralblatt MATH identifier

Primary: 60G50: Sums of independent random variables; random walks
Secondary: 05C81: Random walks on graphs 60J55: Local time and additive functionals 60F10: Large deviations

continuous-time random walk random conductances randomized Laplace operator large deviations Donsker-Varadhan rate function

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König, Wolfgang; Salvi, Michele; Wolff, Tilman. Large deviations for the local times of a random walk among random conductances. Electron. Commun. Probab. 17 (2012), paper no. 10, 11 pp. doi:10.1214/ECP.v17-1820. https://projecteuclid.org/euclid.ecp/1465263143

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