Cox JT, Greven A (1990)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 1990
Publisher: Springer Verlag (Germany)
Book Volume: 85
Pages Range: 195-237
Journal Issue: 2
DOI: 10.1007/BF01277982
We consider the problem of comparing large finite and infinite systems with locally interacting components, and present a general comparison scheme for the case when the infinite system is nonergodic. We show that this scheme holds for some specific models. One of these is critical branching random walk on Z. Let η denote this system, and let η denote a finite version of η defined on the torus [-N, N]∩Z. For d≧3 we prove that for stationary, shift ergodic initial measures with density θ, that if T(N)→∞ and T(N)/(2 N+1) →s∈[0,∞] as N→∞, then[Figure not available: see fulltext.] {v}, θ≧0 is the set of extremal invariant measures for the infinite system η and Q is the transition function of Feller's branching diffusion. We prove several extensions and refinements of this result. The other systems we consider are the voter model and the contact process. © 1990 Springer-Verlag.
APA:
Cox, J.T., & Greven, A. (1990). On the long term behavior of some finite particle systems. Probability Theory and Related Fields, 85(2), 195-237. https://dx.doi.org/10.1007/BF01277982
MLA:
Cox, J. Theodore, and Andreas Greven. "On the long term behavior of some finite particle systems." Probability Theory and Related Fields 85.2 (1990): 195-237.
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