Self-avoiding walks in quenched random environments

1991 ◽  
Vol 64 (3-4) ◽  
pp. 541-578 ◽  
Author(s):  
P. Le Doussal ◽  
J. Machta
Keyword(s):  
Random Environments ◽  
Quenched Random Environments ◽  
Self Avoiding Walks

Self-avoiding walks and manifolds in random environments

1990 ◽  
Vol 41 (10) ◽  
pp. 5345-5356 ◽  
Author(s):  
J. Machta ◽  
T. R. Kirkpatrick
Keyword(s):  
Random Environments ◽  
Self Avoiding Walks

On calculating extinction probabilities for branching processes in random environments

1969 ◽  
Vol 6 (03) ◽  
pp. 478-492 ◽  
Author(s):  
William E. Wilkinson
Keyword(s):  
Generating Functions ◽  
Infinite Sequence ◽  
Branching Processes ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Random Environments ◽  
Real Numbers ◽  
Discrete Time Markov Chain ◽  
Extinction Probabilities ◽  
Image Position

Consider a discrete time Markov chain {Zn } whose state space is the non-negative integers and whose transition probability matrix ║Pij ║ possesses the representation where {Pr }, r = 1,2,…, is a finite or denumerably infinite sequence of non-negative real numbers satisfying , and , is a corresponding sequence of probability generating functions. It is assumed that Z 0 = k, a finite positive integer.

scholarly journals Two-dimensional self-avoiding walks on a cylinder

1999 ◽  
Vol 59 (1) ◽  
pp. R16-R19 ◽  
Author(s):  
Helge Frauenkron ◽  
Maria Serena Causo ◽  
Peter Grassberger
Keyword(s):  
Two Dimensional ◽  
Self Avoiding Walks

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.

Sign in / Sign up

Export Citation Format

Share Document