Open Access
2008 Existence and spatial limit theorems for lattice and continuum particle systems
Mathew D. Penrose
Probab. Surveys 5: 1-36 (2008). DOI: 10.1214/07-PS112


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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Mathew D. Penrose. "Existence and spatial limit theorems for lattice and continuum particle systems." Probab. Surveys 5 1 - 36, 2008.


Published: 2008
First available in Project Euclid: 3 April 2008

zbMATH: 1189.60183
MathSciNet: MR2395152
Digital Object Identifier: 10.1214/07-PS112

Primary: 60F17 , 60K35

Keywords: functional central limit theorem , Interacting particle system , point process

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.5 • 2008
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