Abstract
Let (S(t),t≥0) be a homogeneous fragmentation of ]0,1[ with no loss of mass. For x∈]0,1[, we say that the fragmentation speed of x is v if and only if, as time passes, the size of the fragment that contains x decays exponentially with rate v. We show that there is v typ>0 such that almost every point x∈]0,1[ has speed v typ. Nonetheless, for v in a certain range, the random set \(G\) v of points of speed v, is dense in ]0,1[, and we compute explicitly the spectrum v→Dim(\(G\) v ) where Dim is the Hausdorff dimension.
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Berestycki, J. Multifractal Spectra of Fragmentation Processes. Journal of Statistical Physics 113, 411–430 (2003). https://doi.org/10.1023/A:1026060516513
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DOI: https://doi.org/10.1023/A:1026060516513