The Annals of Probability

Coincidence of Lyapunov exponents for random walks in weak random potentials

Markus Flury

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We investigate the free energy of nearest-neighbor random walks on ℤd, 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≥4, at which we show that quenched and annealed Lyapunov exponents are equal as soon as the strength of the potential is small enough.

Article information

Ann. Probab., Volume 36, Number 4 (2008), 1528-1583.

First available in Project Euclid: 29 July 2008

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Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments
Secondary: 34D08: Characteristic and Lyapunov exponents 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Random walk random potential Lyapunov exponents interacting path potential


Flury, Markus. Coincidence of Lyapunov exponents for random walks in weak random potentials. Ann. Probab. 36 (2008), no. 4, 1528--1583. doi:10.1214/00-AOP368.

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