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2012 Large deviations for the local times of a random walk among random conductances
Wolfgang König, Michele Salvi, Tilman Wolff
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Electron. Commun. Probab. 17: 1-11 (2012). DOI: 10.1214/ECP.v17-1820


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.


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Wolfgang König. Michele Salvi. Tilman Wolff. "Large deviations for the local times of a random walk among random conductances." Electron. Commun. Probab. 17 1 - 11, 2012.


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

zbMATH: 1247.60064
MathSciNet: MR2892409
Digital Object Identifier: 10.1214/ECP.v17-1820

Primary: 60G50
Secondary: 05C81 , 60F10 , 60J55

Keywords: Continuous-time random walk , Donsker-Varadhan rate function , large deviations , Random conductances , randomized Laplace operator


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