Localization for Branching Random Walks in Random Environment

dc.creatorHu, Yueyun
dc.creatorYoshida, Nobuo
dc.date2007-12-05
dc.date.accessioned2026-07-07T08:47:24Z
dc.date.available2026-07-07T08:47:24Z
dc.descriptionWe consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total population grows as fast as its expectation with strictly positive probability. If,on the other hand, $d \le 2$, or the environment is ``random enough", then the total population grows strictly slower than its expectation almost surely. We show the equivalence between the slow population growth and a natural localization property in terms of "replica overlap". We also prove a certain stronger localization property, whenever the total population grows strictly slower than its expectation almost surely.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/0712.0649
dc.identifierhttp://arxiv.org/abs/0712.0649
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/143587
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K37 (Primary); 60F05, 60J80, 60K35, 82D30 (Secondary)
dc.titleLocalization for Branching Random Walks in Random Environment
dc.typetext

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