SLLN and annealed CLT for random walks in I.I.D. random environment on Cayley trees

2021 ◽  
Author(s):  
Siva Athreya ◽  
Antar Bandyopadhyay ◽  
Amites Dasgupta ◽  
Neeraja Sahasrabudhe
Keyword(s):  
Random Walks ◽  
Random Environment ◽  
Cayley Trees

scholarly journals Random walks in I.I.D. random environment on Cayley trees

2014 ◽  
Vol 92 ◽  
pp. 39-44 ◽  
Author(s):  
Siva Athreya ◽  
Antar Bandyopadhyay ◽  
Amites Dasgupta
Keyword(s):  
Random Walks ◽  
Random Environment ◽  
Cayley Trees

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.

Computer Simulations for Some One-Dimensional Models of Random Walks in Fluctuating Random Environment

2005 ◽  
Vol 121 (3-4) ◽  
pp. 361-372 ◽  
Author(s):  
C. Boldrighini ◽  
G. Cosimi ◽  
S. Frigio ◽  
A. Pellegrinotti
Keyword(s):  
Random Walks ◽  
Computer Simulations ◽  
Random Environment ◽  
One Dimensional ◽  
Dimensional Models

scholarly journals On slowdown and speedup of transient random walks in random environment

2009 ◽  
Vol 147 (1-2) ◽  
pp. 43-88 ◽  
Author(s):  
Alexander Fribergh ◽  
Nina Gantert ◽  
Serguei Popov
Keyword(s):  
Random Walks ◽  
Random Environment

The almost sure central limit theorem for one-dimensional nearest-neighbour random walks in a space-time random environment

2004 ◽  
Vol 41 (01) ◽  
pp. 83-92 ◽  
Author(s):  
Jean Bérard
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Walks ◽  
Central Limit ◽  
Random Environment ◽  
Space Time ◽  
Nearest Neighbour ◽  
One Dimensional ◽  
The Central Limit Theorem ◽  
Almost All

The central limit theorem for random walks on ℤ in an i.i.d. space-time random environment was proved by Bernabeiet al.for almost all realization of the environment, under a small randomness assumption. In this paper, we prove that, in the nearest-neighbour case, when the averaged random walk is symmetric, the almost sure central limit theorem holds for anarbitrarylevel of randomness.

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