Local Bootstrap Percolation

Simple item page
dc.creatorGravner, Janko
dc.creatorHolroyd, Alexander E.
dc.date2008-06-13
dc.date.accessioned2026-07-07T09:44:31Z
dc.date.available2026-07-07T09:44:31Z
dc.descriptionWe study a variant of bootstrap percolation in which growth is restricted to a single active cluster. Initially there is a single active site at the origin, while other sites of Z^2 are independently occupied with small probability p, otherwise empty. Subsequently, an empty site becomes active by contact with 2 or more active neighbors, and an occupied site becomes active if it has an active site within distance 2. We prove that the entire lattice becomes active with probability exp[alpha(p)/p], where alpha(p) is between -pi^2/9 + c sqrt p and pi^2/9 + C sqrt p (-log p)^3. This corrects previous numerical predictions for the scaling of the correction term.
dc.description19 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0806.2313
dc.identifierhttp://arxiv.org/abs/0806.2313
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162904
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35; 82B43
dc.titleLocal Bootstrap Percolation
dc.typetext

Files

Collections

arXiv