Super-Brownian Limits of Voter Model Clusters
Super-Brownian Limits of Voter Model Clusters
复制标题
选民模型集群的超布朗极限
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
M. Bramson
中科院分区：
文献类型：
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作者：
Jean;J. Cox;M. Bramson
投票者模型是一种标准的相互作用粒子系统。该过程的两个相关问题是在大时间t之后，针对与站点0共享相同意见的站点集合分析其行为，以及(2)具有最初在0处的意见。Sawyer(1979)和Bramson and Griffeath(1980)给出了关于这些集合大小的结果。在这里，我们研究了d≥2中这些集的空间结构，我们证明了这些空间结构在适当的归一化后收敛到与超布朗运动有关的量。Cox，Durrett和Perkins(2000)的主要定理是这些结果的重要工具。
The voter model is one of the standard interacting particle systems. Two related problems for this process are to analyze its behavior, after large times t, for the sets of sites (1) sharing the same opinion as the site 0, and (2) having the opinion that was originally at 0. Results on the sizes of these sets were given by Sawyer (1979) and Bramson and Griffeath (1980). Here, we investigate the spatial structure of these sets in d ≥ 2, which we show converge to quantities associated with super-Brownian motion, after suitable normalization. The main theorem from Cox, Durrett and Perkins (2000) serves as an important tool for these results.