The Annals of Probability
- Ann. Probab.
- Volume 36, Number 4 (2008), 1528-1583.
Coincidence of Lyapunov exponents for random walks in weak random potentials
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.
Ann. Probab., Volume 36, Number 4 (2008), 1528-1583.
First available in Project Euclid: 29 July 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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]
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