Multifractal spectra and precise rates of decay in homogeneous fragmentation

Details Multifractal spectra and precise rates of decay in homogeneous fragmentation Multifractal spectra and precise rates of decay in homogeneous fragmentation

2006-02-03

arxiv.org/abs/math/0602065v3

Mathematics

Probability

Scientific paper

We consider a mass-conservative fragmentation of the unit interval. The main
purpose of this work is to specify the Hausdorff dimension of the set of
locations having exactly an exponential decay. The study relies on an additive
martingale which arises naturally in this setting, and a class of L\'evy
processes constrained to stay in a finite interval.

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