WIAS Preprint No. 1605, (2011)

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



Authors

  • König, Wolfgang
  • Salvi, Michele
  • Wolff, Tilman

2010 Mathematics Subject Classification

  • 60J65 60J55 60F10

Keywords

  • continuous-time random walk, random conductances, randomly perturbed Laplace operator, large deviations, Donsker--Varadhan rate function

Abstract

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 $Z^d$ in the spirit of Donsker-Varadhan citeDV75. 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 randomly perturbed negative Laplace operator in the domain.

Appeared in

  • Electron. Comm. Probab., 17 (2012) pp. 1--11.

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