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

2005/02/15 by Alexis Devulder, Devulder, Alexis
Decision Sciences · Mathematics · #Markov Chains and Monte Carlo Methods #Probability and Risk Models #Stochastic processes and statistical mechanics #math.PR #msc:60F10 #msc:60J60 #msc:60K37

paper · pdf · doi:10.48550/arxiv.math/0502316

arxiv created 2005/02/15 · arxiv updated 2009/12/01

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→ 0⁺(I_η^q)''(θ)=+∞, 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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