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

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

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.

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 Random Walk on the Incipient Infinite Cluster for Oriented Percolation in High Dimensions

2008 ◽  
Vol 278 (2) ◽  
pp. 385-431 ◽  
Author(s):  
Martin T. Barlow ◽  
Antal A. Járai ◽  
Takashi Kumagai ◽  
Gordon Slade
Keyword(s):  
Random Walk ◽  
Oriented Percolation ◽  
High Dimensions ◽  
Infinite Cluster ◽  
Incipient Infinite Cluster

scholarly journals Positive association of the oriented percolation cluster in randomly oriented graphs

2019 ◽  
Vol 28 (06) ◽  
pp. 811-815
Author(s):  
François Bienvenu
Keyword(s):  
Elementary Proof ◽  
Short Note ◽  
Positive Association ◽  
Percolation Cluster ◽  
Oriented Percolation ◽  
Oriented Graphs ◽  
The Family ◽  
Oriented Path ◽  
Vertex Set ◽  
Advanced Tool

AbstractConsider any fixed graph whose edges have been randomly and independently oriented, and write {S ⇝} to indicate that there is an oriented path going from a vertex s ∊ S to vertex i. Narayanan (2016) proved that for any set S and any two vertices i and j, {S ⇝ i} and {S ⇝ j} are positively correlated. His proof relies on the Ahlswede–Daykin inequality, a rather advanced tool of probabilistic combinatorics.In this short note I give an elementary proof of the following, stronger result: writing V for the vertex set of the graph, for any source set S, the events {S ⇝ i}, i ∊ V, are positively associated, meaning that the expectation of the product of increasing functionals of the family {S ⇝ i} for i ∊ V is greater than the product of their expectations.

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