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October 2001 A Central Limit Theorem With Applications to Percolation, Epidemics and Boolean Models
Mathew D. Penrose
Ann. Probab. 29(4): 1515-1546 (October 2001). DOI: 10.1214/aop/1015345760

Abstract

Suppose $X = (X_x)_{x\in\mathbb{Z}^d}$ is a white noise process, and $H (B)$, defined for finite subsets $B$ of $\math{Z}^d$, is determined in a stationary way by the restriction of $X$ to $B$. Using a martingale approach, we prove a central limit theorem (CLT) for $H$ as $B$ becomes large, subject to $H$ satisfying a “stabilization” condition (the effect of changing $X _x$ at a single site needs to be local). This CLT is then applied to component counts for percolation and Boolean models, to the size of the big cluster for percolation on a box, and to the final size of a spatial epidemic.

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Mathew D. Penrose. "A Central Limit Theorem With Applications to Percolation, Epidemics and Boolean Models." Ann. Probab. 29 (4) 1515 - 1546, October 2001. https://doi.org/10.1214/aop/1015345760

Information

Published: October 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1044.60015
MathSciNet: MR1880230
Digital Object Identifier: 10.1214/aop/1015345760

Subjects:
Primary: 60D05, 60F05
Secondary: 60K35

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 4 • October 2001
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