The existence of quermass-interaction processes for nonlocally stable interaction and nonbounded convex grains
Dereudre David
Source: Adv. in Appl. Probab. Volume 41, Number 3
(2009), 664-681.
Abstract
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.
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Keywords: Stochastic geometry; Boolean model; germ--grain model; Gibbs point process; quermass-interaction process
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aap/1253281059
Digital Object Identifier: doi:10.1239/aap/1253281059
Zentralblatt MATH identifier: 05625063
Mathematical Reviews number (MathSciNet): MR2571312
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