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

Hermine Biermé; Anne Estrade

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arXiv · math/0505635

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

Hermine Biermé·Anne Estrade

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Abstract

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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Hermine Biermé, Anne Estrade. 2005-10-27. Poisson overlapping microballs: self-similarity and X-ray images. https://arxiv.org/abs/math/0505635

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