RANDOM WALK ON ANISOTROPICALLY GENERATED PERCOLATION CLUSTER AND ANISOTROPIC RANDOM WALK ON PERCOLATION CLUSTER

1989 ◽  
Vol 03 (10) ◽  
pp. 765-770
Author(s):  
C.S. KIM ◽  
MIN-HO LEE
Keyword(s):  
Random Walk ◽  
Fractal Dimensionality ◽  
Percolation Cluster ◽  
Asymptotic Convergence ◽  
Spectral Dimensionality

We studied two subjects related to anisotropy: random walk on percolation cluster having anisotropy (RWAC) and direction dependent (anisotropic) random walk on percolation cluster (AWIC). We find that the anisotropy of the cluster has only time-delaying effect on asymptotic convergence of the spectral dimensionality ds and fractal dimensionality of walk dw, however, the anisotropy of the walk results in lower spectral dimensionality and higher fractal dimensionality, as anisotropy grows larger.

Random walk in a percolation cluster: external field dependence

1991 ◽  
Vol 24 (3) ◽  
pp. 735-740
Author(s):  
Jae Woo Lee ◽  
Ho Chui Kim ◽  
Jong-Jean Kim
Keyword(s):  
Random Walk ◽  
External Field ◽  
Field Dependence ◽  
Percolation Cluster

scholarly journals Generation of percolation cluster perimeters by a random walk

1984 ◽  
Vol 17 (15) ◽  
pp. 3009-3017 ◽  
Author(s):  
R M Ziff ◽  
P T Cummings ◽  
G Stells
Keyword(s):  
Random Walk ◽  
Percolation Cluster

scholarly journals Directed random walk on the backbone of an oriented percolation cluster

2013 ◽  
Vol 18 (0) ◽  
Author(s):  
Matthias Birkner ◽  
Jiri Cerny ◽  
Andrej Depperschmidt ◽  
Nina Gantert
Keyword(s):  
Random Walk ◽  
Percolation Cluster ◽  
Oriented Percolation

scholarly journals The Speed of Simple Random Walk and Anchored Expansion on Percolation Clusters: an Overview

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Dayue Chen ◽  
Yuval Peres
Keyword(s):  
Random Walk ◽  
Percolation Cluster ◽  
Simple Random Walk ◽  
Random Perturbations ◽  
Exponential Tail ◽  
Infinite Cluster ◽  
Lamplighter Group ◽  
Percolation Clusters ◽  
Percolation Parameter ◽  
International Audience

International audience Benjamini, Lyons and Schramm (1999) considered properties of an infinite graph $G$, and the simple random walk on it, that are preserved by random perturbations. To address problems raised by those authors, we study simple random walk on the infinite percolation cluster in Cayley graphs of certain amenable groups known as "lamplighter groups''.We prove that zero speed for random walk on a lamplighter group implies zero speed for random walk on an infinite cluster, for any supercritical percolation parameter $p$. For $p$ large enough, we also establish the converse. We prove that if $G$ has a positive anchored expansion constant then so does every infinite cluster of independent percolation with parameter $p$ sufficiently close to 1; We also show that positivity of the anchored expansion constant is preserved under a random stretch if, and only if, the stretching law has an exponential tail.

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