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

• 成果类型: Article
• 署名作者: Burdzy, Krzysztof; Quastel, Jeremy
• 署名单位: University of Washington; University of Washington Seattle; University of Toronto
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000511
• 发表日期: 2006
• 页码: 2382-2405
• 关键词: viot type system; spatial segregation; laplacian; eigenfunctions; BOUNDARY; domains; limit

摘要

We consider two species of particles performing random walks in a domain in 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.