MULTITYPE THRESHOLD GROWTH: CONVERGENCE TO POISSON-VORONOI TESSELLATIONS
成果类型：
Article
署名作者：
Gravner, Janko; Griffeath, David
署名单位：
University of California System; University of California Davis; University of Wisconsin System; University of Wisconsin Madison
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1997
页码：
615-647
关键词：
摘要：
A Poisson-Voronoi tessellation (PVT) is a tiling of the Euclidean plane in which centers of individual tiles constitute a Poisson field and each tile comprises the locations that are closest to a given center with respect to a prescribed norm. Many spatial systems in which rare, randomly distributed centers compete for space should be well approximated by a PVT. Examples that we can handle rigorously include multitype threshold vote automata, in which k different camps compete for voters stationed on the two-dimensional lattice. According to the deterministic, discrete-time update rule, a voter changes affiliation only to that of a unique opposing camp having more than theta representatives in the voter's neighborhood. We establish a PVT limit for such dynamics started from completely random configurations, as the number of camps becomes large, so that the density of initial pockets of consensus tends to 0. Our methods combine nucleation analysis, Poisson approximation, and shape theory.