Directed percolation and random walk

Simple item page
dc.creatorGrimmett, Geoffrey
dc.creatorHiemer, Philipp
dc.date2001-08-08
dc.date.accessioned2026-07-07T04:42:55Z
dc.date.available2026-07-07T04:42:55Z
dc.descriptionTechniques of `dynamic renormalization', developed earlier for undirected percolation and the contact model, are adapted to the setting of directed percolation, thereby obtaining solutions of several problems for directed percolation on $Z^d$ where $d \ge 2$. The first new result is a type of uniqueness theorem: for every pair $x$ and $y$ of vertices which lie in infinite open paths, there exists almost surely a third vertex $z$ which is joined to infinity and which is attainable from $x$ and $y$ along directed open paths. Secondly, it is proved that a random walk on an infinite directed cluster is transient, almost surely, when $d \ge 3$. And finally, the block arguments of the paper may be adapted to systems with infinite range, subject to certain conditions on the edge probabilities.
dc.identifierhttps://arxiv.org/abs/math/0108062
dc.identifierhttp://arxiv.org/abs/math/0108062
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61993
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35, 82B43, 60G50, 60K37
dc.titleDirected percolation and random walk
dc.typetext

Files

Collections

arXiv