晶格和连续体粒子系统的存在性和空间极限定理

IF 1.3 Q2 STATISTICS & PROBABILITY
M. Penrose
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引用次数: 39

摘要

我们给出了具有局域相互作用和跳跃速率有界但在每个点的状态空间不紧致的相互作用粒子系统的一般存在性结果。我们允许一个站点上的跳转事件影响其相邻站点的状态。本文给出了zd的递增子立方体族上的加性集函数的一个大数定律和泛函中心极限定理。我们讨论了具有粒子出生、死亡和跳跃的标记空间点过程的应用,特别是连续体和晶格弹道沉积以及随机松散球体堆积的顺序模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Existence and spatial limit theorems for lattice and continuum particle systems
We give a general existence result for interacting particle systems with local interactions and bounded jump rates but noncompact state space at each site. We allow for jump events at a site that affect the state of its neighbours. We give a law of large numbers and functional central limit theorem for additive set functions taken over an increasing family of subcubes of Z d . We discuss application to marked spatial point processes with births, deaths and jumps of particles, in particular examples such as continuum and lattice ballistic deposition and a sequential model for random loose sphere packing.
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来源期刊
Probability Surveys
Probability Surveys STATISTICS & PROBABILITY-
CiteScore
4.70
自引率
0.00%
发文量
9
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