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The volume fraction of a non--overlapping germ--grain model

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	The volume fraction of a non--overlapping germ--grain model
2.	Creator	Author's name, affiliation, country	Jenny Andersson; Mathematical Sciences, Chalmers University of Technology
2.	Creator	Author's name, affiliation, country	Olle Häggström; Mathematical Sciences, Chalmers University of Technology
2.	Creator	Author's name, affiliation, country	Marianne Månsson; Mathematical Sciences, Chalmers University of Technology
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	volume fraction, germ-grain model, dead leaves model
3.	Subject	Subject classification	60D05
4.	Description	Abstract	We discuss the volume fraction of a model of non--overlapping convex grains. It is obtained from thinning a Poisson process where each point has a weight and is the centre of a grain, by removing any grain that is overlapped by one of larger or equal weight. In the limit as the intensity of the Poisson process tends to infinity, the model can be identified with the intact grains in the dead leaves model if the weights are independent of the grain sizes. In this case we can show that the volume fraction is at most $1/2^d$ for $d=1$ or $2$ if the shape is fixed, but the size and the orientation are random. The upper bound is achieved for centrally symmetric sets of the same size and orientation. For general $d$ we can show the upper bound, $1/2^d$, for spherical grains with two--point radius distribution. If dependence between weight and size is allowed, it is possible to achieve a volume fraction arbitrarily close to one.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	The Swedish Research Council
7.	Date	(YYYY-MM-DD)	2006-06-13
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1197
10.	Identifier	Digital Object Identifier	10.1214/ECP.v11-1197
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 11
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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