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.
Highlights
any B-valued sequence (An) interacting particle system may be informally described as ‘a Markov process consisting of countably many pure-jump processes that interact by modifying each other’s transition rates’ ([24], p. 641)
In the present work we give a general construction for interacting particle systems where we assume only that the constituent pure-jump processes live in a separable complete metric space that is not required to be compact
The results of the present paper extend known existence and limit results to functional central limit theorems, and to deposition models allowing for displacement whereby an incoming particle may influence the positions of existing particles
Summary
An interacting particle system may be informally described as ‘a Markov process consisting of countably many pure-jump processes that interact by modifying each other’s transition rates’ ([24], p. 641). We refer to these processes as spatial birth, death, migration and displacement processes In this type of continuum model, the ‘state’ at a site in Zd refers to the configuration of points in a patch of Rd. Our results add to previous work in [26; 27; 33; 52] on the theory of evolving point process.
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