Limit law for transition probabilities and moderate deviations for Sinai's random walk in random environment

2003 ◽  
Vol 126 (4) ◽  
pp. 571-609 ◽  
Author(s):  
Francis Comets ◽  
Serguei Popov
Keyword(s):  
Random Walk ◽  
Random Environment ◽  
Transition Probabilities ◽  
Moderate Deviations

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.

scholarly journals Large and moderate deviations for a -valued branching random walk with a random environment in time

Stochastics ◽  
2019 ◽  
Vol 92 (6) ◽  
pp. 944-968
Author(s):  
Chunmao Huang ◽  
Xin Wang ◽  
Xiaoqiang Wang
Keyword(s):  
Random Walk ◽  
Random Environment ◽  
Moderate Deviations ◽  
Branching Random Walk

Random walk in a random environment with correlated sites

2001 ◽  
Vol 38 (04) ◽  
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 Z d . 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.

scholarly journals Ballisticity conditions for random walk in random environment

2010 ◽  
Vol 150 (1-2) ◽  
pp. 61-75 ◽  
Author(s):  
A. Drewitz ◽  
A. F. Ramírez
Keyword(s):  
Random Walk ◽  
Random Environment

scholarly journals Random walk in a high density dynamic random environment

2014 ◽  
Vol 25 (4) ◽  
pp. 785-799 ◽  
Author(s):  
Frank den Hollander ◽  
Harry Kesten ◽  
Vladas Sidoravicius
Keyword(s):  
Random Walk ◽  
Random Environment ◽  
High Density ◽  
Density Dynamic

scholarly journals Random walk in cooling random environment: ergodic limits and concentration inequalities

2019 ◽  
Vol 24 (0) ◽  
Author(s):  
Luca Avena ◽  
Yuki Chino ◽  
Conrado da Costa ◽  
Frank den Hollander
Keyword(s):  
Random Walk ◽  
Random Environment ◽  
Concentration Inequalities
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