Existence and spatial limit theorems for lattice and continuum particle systems

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.

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

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• Spatial birth and death processes as solutions of stochastic equations
• Dynamics of Nonequilibrium Deposition
• Existence of the zero range process and a deposition model with superlinear growth rates
• Exact and approximate results for deposition and annihilation processes on graphs
• Strong law of large numbers for the interface in ballistic deposition
• Mathematics of random growing interfaces
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• Stochastic stability of traffic maps
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• A Markov process for an infinite interacting particle system in the continuum
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