Limiting shapes for deterministic centrally seeded growth models

Simple item page
dc.creatorFey, Anne
dc.creatorRedig, Frank
dc.date2007-02-15
dc.date2007-10-04
dc.date.accessioned2026-07-07T10:09:14Z
dc.date.available2026-07-07T10:09:14Z
dc.descriptionWe study the rotor router model and two deterministic sandpile models. For the rotor router model in $\mathbb{Z}^d$, Levine and Peres proved that the limiting shape of the growth cluster is a sphere. For the other two models, only bounds in dimension 2 are known. A unified approach for these models with a new parameter $h$ (the initial number of particles at each site), allows to prove a number of new limiting shape results in any dimension $d \geq 1$. For the rotor router model, the limiting shape is a sphere for all values of $h$. For one of the sandpile models, and $h=2d-2$ (the maximal value), the limiting shape is a cube. For both sandpile models, the limiting shape is a sphere in the limit $h \to -\infty$. Finally, we prove that the rotor router shape contains a diamond.
dc.description18 pages, 3 figures, some errors corrected and more explanation added, to appear in Journal of Statistical Physics
dc.identifierhttps://arxiv.org/abs/math/0702450
dc.identifierhttp://arxiv.org/abs/math/0702450
dc.identifierJournal of Statistical Physics (2008) 130: 579-597
dc.identifierdoi:10.1007/s10955-007-9450-6
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171257
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35
dc.titleLimiting shapes for deterministic centrally seeded growth models
dc.typetext

Files

Collections

arXiv