Stable Distributions in Stochastic Fragmentation

Details Stable Distributions in Stochastic Fragmentation Stable Distributions in Stochastic Fragmentation

2001-08-31

arxiv.org/abs/cond-mat/0108547v1

J. Phys. A 37, 2863 (2004)

Physics

Condensed Matter

Statistical Mechanics

11 pages, 5 figures

Scientific paper

10.1088/0305-4470/37/8/002

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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