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

Penrose, Mathew D.

Probab. Surv. 5, 1-36 (2008).

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.

MSC:

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

Keywords:

interacting particle system; functional central limit theorem; point process