2007/03/31 by Mathew D. Penrose · 2 citations
Mathematics · #Bounded function #Central limit theorem #Interacting particle system #Jump #Lattice (music) #Law of large numbers #Limit (mathematics) #Mathematical analysis #Mathematics #Particle system #Physics #Point processes and geometric inequalities #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Random variable #Statistical physics #Statistics #Stochastic processes and statistical mechanics #math.PR #msc:60F17 #msc:60K35
paper · pdf · doi:10.1214/07-ps112
published as Probability Surveys 2008, Vol. 5, 1-36 · 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)
openalex publication_date 2008/01/01 · arxiv created 2008/04/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Zd. 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.