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Coincidence of Lyapunov exponents for random walks in weak random potentials

Markus Flury
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Abstract

We investigate the free energy of nearest-neighbor random walks on $\mathbb{Z}^d$, endowed with a drift along the first axis and evolving in a nonnegative random potential given by i.i.d. random variables. Our main result concerns the ballistic regime in dimensions $d\geq4$, at which we show that quenched and annealed Lyapunov exponents are equal as soon as the strength of the potential is small enough.

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Markus Flury. 2008-08-27. Coincidence of Lyapunov exponents for random walks in weak random potentials. https://doi.org/10.1214/00-aop368

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