UNSPECIFIED (1999) Quermass-interaction processes: Conditions for stability. ADVANCES IN APPLIED PROBABILITY, 31 (2). pp. 315-342. ISSN 0001-8678

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Abstract

We consider a class of random point and germ-grain processes, obtained using a rather natural weighting procedure. Given a Poisson point process, on each point one places a grain, a (possibly random) compact convex set. Let Xi be the union of all grains. One can now construct new processes whose density is derived from an exponential of a linear combination of quermass functionals of Xi. If only the area functional is used, then the area-interaction point process is recovered. New point processes arise if we include the perimeter length functional, or the Euler functional (number of components minus number of holes). The main question addressed by the paper is that of when the resulting point process is well-defined: geometric arguments are used to establish conditions for the point process to be stable in the sense of Ruelle.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	ADVANCES IN APPLIED PROBABILITY
Publisher:	APPLIED PROBABILITY TRUST
ISSN:	0001-8678
Date:	June 1999
Volume:	31
Number:	2
Number of Pages:	28
Page Range:	pp. 315-342
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/14039

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