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Limit theorem and large deviation principle for the Voronoi tessellation generated by a Gibbs point process

Part of: Limit theorems Special processes

Published online by Cambridge University Press:  01 July 2016

Koji Kuroda  and
Hideki Tanemura
Koji Kuroda*
Affiliation:
Keio University
Hideki Tanemura*
Affiliation:
Chiba University
*
∗Postal address: Department of Mathematics, Keio University, Hiyosi 3–14–1, Yokohama 223, Japan.
∗∗Postal address: Department of Mathematics, Chiba University, Yayoicho 1–33, Chiba 260, Japan.
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Abstract

The Voronoi tessellation generated by a Gibbs point process is considered. Using the algebraic formalism of polymer expansion, the limit theorem and the large deviation principle for the number of Voronoi vertices are proved.

Keywords

GIBBS MEASURECLUSTER EXPANSIONPOLYMER EXPANSION

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60F05: Central limit and other weak theorems 60F10: Large deviations
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 1 , March 1992 , pp. 45 - 70
Copyright
Copyright © Applied Probability Trust 1992 

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