The Annals of Probability

A Limit Theorem for a Class of Interacting Particle Systems

Italo Simonelli

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Abstract

Let $S$ be a countable set and $\Lambda$ the collection of all subsets of $S$. We consider interacting particle systems (IPS) $\{\eta_k\}$ on $\Lambda$, with duals $\{\tilde\eta_t\}$ and duality equation $P\lbrack |\eta^\zeta_t \cap A| \operatorname{odd} = \tilde{P}\lbrack |\tilde\eta_t^A \cap \zeta| \operatorname{odd} \rbrack, \zeta, A \subset S, A$ finite Under certain conditions we find all the extreme invariant distributions that arise as limits of translation invariant initial configurations. Specific systems will be considered. A new property of the annihilating particle model is then used to prove a limiting relation between the annihilating and coalescing particle models.

Article information

Source
Ann. Probab., Volume 23, Number 1 (1995), 141-156.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988380

Digital Object Identifier
doi:10.1214/aop/1176988380

Mathematical Reviews number (MathSciNet)
MR1330764

Zentralblatt MATH identifier
0833.60094

JSTOR
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Cancellative systems duality equation annihilation

Citation

Simonelli, Italo. A Limit Theorem for a Class of Interacting Particle Systems. Ann. Probab. 23 (1995), no. 1, 141--156. doi:10.1214/aop/1176988380. https://projecteuclid.org/euclid.aop/1176988380


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