Poisson overlapping microballs: self-similarity and X-ray images

Details Poisson overlapping microballs: self-similarity and X-ray images Poisson overlapping microballs: self-similarity and X-ray images

2005-05-30

arxiv.org/abs/math/0505635v2

Mathematics

Probability

A multifractional case is investigated and reference [10] is added. Former title: "Poisson microballs: self-similarity and dir

Scientific paper

We study a random field obtained by counting the number of balls containing each point, when overlapping balls are thrown at random according to a Poisson random measure. We are particularly interested in the local asymptotical self-similarity (lass) properties of the field, as well as the action of X-ray transforms. We discover two different lass properties when considering the asymptotic either "in law" or "on the second order moment" and prove a relationship between the lass behavior of the field and the lass behavior of its X-ray transform. We also describe a microscopic process which leads to a multifractional behavior. These results can be exploited to model and analyze granular media, images or connections network.

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