Coincidence of Lyapunov exponents for random walks in weak random potentials

Details Coincidence of Lyapunov exponents for random walks in weak random potentials Coincidence of Lyapunov exponents for random walks in weak random potentials

2006-08-14

arxiv.org/abs/math/0608357v3

Annals of Probability 2008, Vol. 36, No. 4, 1528-1583

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/00-AOP368 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/00-AOP368

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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