Random soups, carpets and fractal dimensions

Details Random soups, carpets and fractal dimensions Random soups, carpets and fractal dimensions

2010-09-24

arxiv.org/abs/1009.4782v1

Mathematics

Probability

To appear in J. London Math. Soc

Scientific paper

We study some properties of a class of random connected planar fractal sets induced by a Poissonian scale-invariant and translation-invariant point process. Using the second-moment method, we show that their Hausdorff dimensions are deterministic and equal to their expectation dimension. We also estimate their low-intensity limiting behavior. This applies in particular to the "conformal loop ensembles" defined via Poissonian clouds of Brownian loops for which the expectation dimension has been computed by Schramm, Sheffield and Wilson.

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