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arXiv · 1404.7051

Lyapunov exponents of random walks in small random potential: the upper bound

Thomas Mountford·Jean-Christophe Mourrat
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Abstract

We consider the simple random walk on $\mathbb{Z}^d$ evolving in a random i.i.d. potential taking values in $[0,+\infty)$. The potential is not assumed integrable, and can be rescaled by a multiplicative factor $λ> 0$. Completing the work started in a companion paper, we give the asymptotic behaviour of the Lyapunov exponents for $d \ge 3$, both annealed and quenched, as the scale parameter $λ$ tends to zero.

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Thomas Mountford, Jean-Christophe Mourrat. 2014-04-28. Lyapunov exponents of random walks in small random potential: the upper bound. https://arxiv.org/abs/1404.7051

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