Stable Distributions in Stochastic Fragmentation

P. L. Krapivsky; E. Ben-Naim; I. Grosse

doi:10.1088/0305-4470/37/8/002

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Stable Distributions in Stochastic Fragmentation

P. L. Krapivsky·E. Ben-Naim·I. Grosse

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Abstract

We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail. Furthermore, the entire range of acceptable values of decay exponent consistent with the length conservation can be realized. We show that the stochastic fragmentation process is non-self-averaging as moments exhibit significant sample-to-sample fluctuations. Additionally, we find that the distributions of the moments and of extremal characteristics possess an infinite set of progressively weaker singularities.

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P. L. Krapivsky, E. Ben-Naim, I. Grosse. 2001-08-31. Stable Distributions in Stochastic Fragmentation. https://doi.org/10.1088/0305-4470%2F37%2F8%2F002

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