scholarly journals Coalescing directed random walks on the backbone of a 1+1-dimensional oriented percolation cluster converge to the Brownian web

2019 ◽  
Vol 16 (2) ◽  
pp. 1029
Author(s):  
Matthias Birkner ◽  
Nina Gantert ◽  
Sebastian Steiber
Keyword(s):  
Random Walks ◽  
Percolation Cluster ◽  
Oriented Percolation

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 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.

scholarly journals Quenched invariance principles for random walks on percolation clusters

2007 ◽  
Vol 463 (2085) ◽  
pp. 2287-2307 ◽  
Author(s):  
P Mathieu ◽  
A Piatnitski
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Invariance Principle ◽  
Percolation Cluster ◽  
Percolation Model ◽  
Symmetric Random Walk ◽  
Invariance Principles ◽  
Percolation Clusters

We consider a supercritical Bernoulli percolation model in , d ≥2, and study the simple symmetric random walk on the infinite percolation cluster. The aim of this paper is to prove the almost sure (quenched) invariance principle for this random walk.

Non-homogeneous Random Walks

2016 ◽  
Author(s):  
Mikhail Menshikov ◽  
Serguei Popov ◽  
Andrew Wade
Keyword(s):  
Random Walks
Sign in / Sign up

Export Citation Format

Share Document