unknown10.1214/EJP.v9-215

Asymptotic laws for nonconservative self-similar fragmentations

Abstract

We consider a self-similar fragmentation process in which the generic particle of size $x$ is replaced at probability rate $x^\alpha$, by its offspring made of smaller particles, where $\alpha$ is some positive parameter. The total of offspring sizes may be both larger or smaller than $x$ with positive probability. We show that under certain conditions the typical size in the ensemble is of the order $t^{-1/\alpha}$ and that the empirical distribution of sizes converges to a random limit which we characterise in terms of the reproduction law

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Last time updated on July 9, 2013View original full text link

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