The Annals of Probability

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 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

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

Dates
First available in Project Euclid: 29 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.aop/1217360978

Digital Object Identifier
doi:10.1214/00-AOP368

Mathematical Reviews number (MathSciNet)
MR2435858

Zentralblatt MATH identifier
1156.60076

Subjects
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]

Keywords
Random walk random potential Lyapunov exponents interacting path potential

Citation

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. https://projecteuclid.org/euclid.aop/1217360978


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