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The existence of quermass-interaction processes for nonlocally stable interaction and nonbounded convex grains

Part of: Equilibrium statistical mechanics Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

David Dereudre
David Dereudre*
Affiliation:
Université de Valenciennes et du Hainaut-Cambrésis
*
∗ Postal address: LAMAV, Université de Valenciennes et du Hainaut-Cambrésis, Le Mont Houy, 59313 Valenciennes Cedex 09, France. Email address: david.dereudre@univ-valenciennes.fr
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Abstract

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We prove the existence of infinite-volume quermass-interaction processes in a general setting of nonlocally stable interaction and nonbounded convex grains. No condition on the parameters of the linear combination of the Minkowski functionals is assumed. The only condition is that the square of the random radius of the grain admits exponential moments for all orders. Our methods are based on entropy and large deviation tools.

Keywords

Stochastic geometryBoolean modelgerm–grain modelGibbs point processquermass-interaction process

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 82B21: Continuum models (systems of particles, etc.)
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 41 , Issue 3 , September 2009 , pp. 664 - 681
Copyright
Copyright © Applied Probability Trust 2009 

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