scholarly journals Current fluctuations of a system of one-dimensional random walks in random environment

2010 ◽  
Vol 38 (6) ◽  
pp. 2258-2294 ◽  
Author(s):  
Jonathon Peterson ◽  
Timo Seppäläinen
Keyword(s):  
Random Walks ◽  
Random Environment ◽  
Current Fluctuations ◽  
One Dimensional

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

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.

scholarly journals Random Walks in a One-Dimensional Lévy Random Environment

2016 ◽  
Vol 163 (1) ◽  
pp. 22-40 ◽  
Author(s):  
Alessandra Bianchi ◽  
Giampaolo Cristadoro ◽  
Marco Lenci ◽  
Marilena Ligabò
Keyword(s):  
Random Walks ◽  
Random Environment ◽  
One Dimensional

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

2004 ◽  
Vol 41 (1) ◽  
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 Bernabei et 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 an arbitrary level of randomness.

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