An annihilating--branching particle model for the heat equation with average temperature zero

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dc.creatorBurdzy, Krzysztof
dc.creatorQuastel, Jeremy
dc.date2005-03-19
dc.date2007-02-28
dc.date.accessioned2026-07-07T07:49:06Z
dc.date.available2026-07-07T07:49:06Z
dc.descriptionWe consider two species of particles performing random walks in a domain in $\mathbb{R}^d$ with reflecting boundary conditions, which annihilate on contact. In addition, there is a conservation law so that the total number of particles of each type is preserved: When the two particles of different species annihilate each other, particles of each species, chosen at random, give birth. We assume initially equal numbers of each species and show that the system has a diffusive scaling limit in which the densities of the two species are well approximated by the positive and negative parts of the solution of the heat equation normalized to have constant $L^1$ norm. In particular, the higher Neumann eigenfunctions appear as asymptotically stable states at the diffusive time scale.
dc.descriptionPublished at http://dx.doi.org/10.1214/009117906000000511 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0503395
dc.identifierhttp://arxiv.org/abs/math/0503395
dc.identifierAnnals of Probability 2006, Vol. 34, No. 6, 2382-2405
dc.identifierdoi:10.1214/009117906000000511
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124726
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60F17, 60K35 (Primary)
dc.titleAn annihilating--branching particle model for the heat equation with average temperature zero
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