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**Harvard**

Andersson, J., Häggström, O. och Månsson, M. (2006) *The Volume Fraction of a Non-overlapping Germ-grain Model*.

** BibTeX **

@article{

Andersson2006,

author={Andersson, Jenny and Häggström, Olle and Månsson, Marianne},

title={The Volume Fraction of a Non-overlapping Germ-grain Model},

journal={Electronic Communications in Probability},

issn={1083-589X},

volume={11},

pages={78-88},

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.},

year={2006},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 24477

A1 Andersson, Jenny

A1 Häggström, Olle

A1 Månsson, Marianne

T1 The Volume Fraction of a Non-overlapping Germ-grain Model

YR 2006

JF Electronic Communications in Probability

SN 1083-589X

VO 11

SP 78

OP 88

AB 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.

LA eng

LK http://publications.lib.chalmers.se/records/fulltext/local_24477.pdf

OL 30