Existence and spatial limit theorems for lattice and continuum particle systems

Details Existence and spatial limit theorems for lattice and continuum particle systems Existence and spatial limit theorems for lattice and continuum particle systems

2007-03-02

arxiv.org/abs/math/0703072v2

Probability Surveys 2008, Vol. 5, 1-36

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-PS112 the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of

Scientific paper

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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