Stable Distributions in Stochastic Fragmentation/H2>
P.L. Krapivsky, E. Ben-Naim, and I.Grosse
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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