Existence and spatial limit theorems for lattice and continuum particle systems. (English) Zbl 1189.60183

Summary: 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 neighbors. We give a law of large numbers and functional central limit theorem for additive set functions taken over an increasing family of subcubes of \(\mathbb Z^d\). We discuss applications 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.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F17 Functional limit theorems; invariance principles
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