Probability Surveys

Existence and spatial limit theorems for lattice and continuum particle systems

Mathew D. Penrose

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Abstract

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.

Article information

Source
Probab. Surveys, Volume 5 (2008), 1-36.

Dates
First available in Project Euclid: 3 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.ps/1207254889

Digital Object Identifier
doi:10.1214/07-PS112

Mathematical Reviews number (MathSciNet)
MR2395152

Zentralblatt MATH identifier
1189.60183

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60F17: Functional limit theorems; invariance principles

Keywords
Interacting particle system functional central limit theorem point process

Citation

Penrose, Mathew D. Existence and spatial limit theorems for lattice and continuum particle systems. Probab. Surveys 5 (2008), 1--36. doi:10.1214/07-PS112. https://projecteuclid.org/euclid.ps/1207254889


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