We solve the problem posed by S.A. Kalikow whether the event that
the $x$-coordinate of a random walk in a two-dimensional random environment
approaches $\infty$ has necessarily probability either zero or one. The answer
is yes if we assume the environment to be i.i.d.and in general no
if we allow the environment to be just stationary and ergodic.
Publié le : 2001-10-14
Classification:
random walk in random environment,
RWRE,
zero-one law,
60K37,
60F20
@article{1015345769,
author = {Zerner, Martin P. W. and Merkl, Franz},
title = {A Zero-One Law for Planar Random walks in Random
Environment},
journal = {Ann. Probab.},
volume = {29},
number = {1},
year = {2001},
pages = { 1716-1732},
language = {en},
url = {http://dml.mathdoc.fr/item/1015345769}
}
Zerner, Martin P. W.; Merkl, Franz. A Zero-One Law for Planar Random walks in Random
Environment. Ann. Probab., Tome 29 (2001) no. 1, pp. 1716-1732. http://gdmltest.u-ga.fr/item/1015345769/