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Some properties of the rate function of quenched large deviations for random walk in random environment

Alexis Devulder
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Abstract

In this paper, we are interested in some questions of Greven and den Hollander about the rate function $I\_η^q$ of quenched large deviations for random walk in random environment. By studying the hitting times of RWRE, we prove that in the recurrent case, $\lim\_{θ\to 0^+}(I\_η^q)''(θ)=+\infty$, which gives an affirmative answer to a conjecture of Greven and den Hollander. We also establish a comparison result between the rate function of quenched large deviations for a diffusion in a drifted Brownian potential, and the rate function for a drifted Brownian motion with the same speed.

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Alexis Devulder. 2005-02-15. Some properties of the rate function of quenched large deviations for random walk in random environment. https://arxiv.org/abs/math/0502316

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