Open Access
October, 1988 Some Limit Theorems for Voter Model Occupation Times
J. T. Cox
Ann. Probab. 16(4): 1559-1569 (October, 1988). DOI: 10.1214/aop/1176991583


Let $\eta_t$ be the (basic) voter model on $\mathbb{Z}^d$. We consider the occupation time functionals $\int^t_0 f(\eta_s)ds$ for certain functions $f$ and initial distributions. The first result is a pointwise ergodic theorem in the case $d = 2$, extending the work of Andjel and Kipnis. The second result is a central limit type theorem for $f(\eta) = \eta(0)$ and initial distributions: (i) $\delta_\eta$, for a class of states $\eta, d \geq 2$, and (ii) $\nu_\theta$, the extremal invariant measures, $d \geq 3$.


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J. T. Cox. "Some Limit Theorems for Voter Model Occupation Times." Ann. Probab. 16 (4) 1559 - 1569, October, 1988.


Published: October, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0656.60105
MathSciNet: MR958202
Digital Object Identifier: 10.1214/aop/1176991583

Primary: 60K35

Keywords: Coalescing random walks , Occupation times , pointwise ergodic theorem , pointwise ergodic theorems , voter model

Rights: Copyright © 1988 Institute of Mathematical Statistics

Vol.16 • No. 4 • October, 1988
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