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.
Publié le : 2008-07-15
Classification:
Random walk,
random potential,
Lyapunov exponents,
interacting path potential,
60K37,
34D08,
60K35
@article{1217360978,
author = {Flury, Markus},
title = {Coincidence of Lyapunov exponents for random walks in weak random potentials},
journal = {Ann. Probab.},
volume = {36},
number = {1},
year = {2008},
pages = { 1528-1583},
language = {en},
url = {http://dml.mathdoc.fr/item/1217360978}
}
Flury, Markus. Coincidence of Lyapunov exponents for random walks in weak random potentials. Ann. Probab., Tome 36 (2008) no. 1, pp. 1528-1583. http://gdmltest.u-ga.fr/item/1217360978/