Random walks and random environments, vol. 2, random environments

1997 ◽  
Vol 87 (3-4) ◽  
pp. 961-962 ◽  
Author(s):  
Jack F. Douglas
Keyword(s):  
Random Walks ◽  
Random Environments

scholarly journals A comparison of random walks in dependent random environments

2016 ◽  
Vol 48 (1) ◽  
pp. 199-214
Author(s):  
Werner R. W. Scheinhardt ◽  
Dirk P. Kroese
Keyword(s):  
Random Walks ◽  
Random Environment ◽  
Moving Average ◽  
Random Environments ◽  
Dependency Structure ◽  
Interesting Behavior

Abstract We provide exact computations for the drift of random walks in dependent random environments, including k-dependent and moving average environments. We show how the drift can be characterized and evaluated using Perron–Frobenius theory. Comparing random walks in various dependent environments, we demonstrate that their drifts can exhibit interesting behavior that depends significantly on the dependency structure of the random environment.

scholarly journals Law of large numbers for non-elliptic random walks in dynamic random environments

2013 ◽  
Vol 123 (1) ◽  
pp. 156-190 ◽  
Author(s):  
F. den Hollander ◽  
R. dos Santos ◽  
V. Sidoravicius
Keyword(s):  
Random Walks ◽  
Law Of Large Numbers ◽  
Random Environments ◽  
Large Numbers

scholarly journals Einstein relation for random walks in random environments

2005 ◽  
Vol 115 (8) ◽  
pp. 1279-1301 ◽  
Author(s):  
T. Komorowski ◽  
S. Olla
Keyword(s):  
Random Walks ◽  
Einstein Relation ◽  
Random Environments

Random walk in a random environment with correlated sites

2001 ◽  
Vol 38 (4) ◽  
pp. 1018-1032 ◽  
Author(s):  
T. Komorowski ◽  
G. Krupa
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Random Field ◽  
Random Environment ◽  
Law Of Large Numbers ◽  
Transition Probabilities ◽  
Direct Application ◽  
Random Environments ◽  
Large Numbers ◽  
Stationary Random Field

We prove the law of large numbers for random walks in random environments on the d-dimensional integer lattice Zd. The environment is described in terms of a stationary random field of transition probabilities on the lattice, possessing a certain drift property, modeled on the Kalikov condition. In contrast to the previously considered models, we admit possible correlation of transition probabilities at different sites, assuming however that they become independent at finite distances. The possible dependence of sites makes impossible a direct application of the renewal times technique of Sznitman and Zerner.

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