Random Walks in Degenerate Random Environments
Canadian journal of mathematics, Tome 66 (2014) no. 5, pp. 1050-1077
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We study the asymptotic behaviour of random walks in i.i.d. random environments on ${{\mathbb{Z}}^{d}}$ . The environments need not be elliptic, so some steps may not be available to the random walker. We prove a monotonicity result for the velocity (when it exists) for any 2-valued environment, and show that this does not hold for 3-valued environments without additional assumptions. We give a proof of directional transience and the existence of positive speeds under strong but non-trivial conditions on the distribution of the environment. Our results include generalisations (to the non-elliptic setting) of 0-1 laws for directional transience and, in 2-dimensions, the existence of a deterministic limiting velocity.
Mots-clés :
60K37, Random walk, non-elliptic random environment, zero-one law, coupling
Holmes, Mark; Salisbury, Thomas S. Random Walks in Degenerate Random Environments. Canadian journal of mathematics, Tome 66 (2014) no. 5, pp. 1050-1077. doi: 10.4153/CJM-2013-017-3
@article{10_4153_CJM_2013_017_3,
author = {Holmes, Mark and Salisbury, Thomas S.},
title = {Random {Walks} in {Degenerate} {Random} {Environments}},
journal = {Canadian journal of mathematics},
pages = {1050--1077},
year = {2014},
volume = {66},
number = {5},
doi = {10.4153/CJM-2013-017-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-017-3/}
}
TY - JOUR AU - Holmes, Mark AU - Salisbury, Thomas S. TI - Random Walks in Degenerate Random Environments JO - Canadian journal of mathematics PY - 2014 SP - 1050 EP - 1077 VL - 66 IS - 5 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-017-3/ DO - 10.4153/CJM-2013-017-3 ID - 10_4153_CJM_2013_017_3 ER -
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