2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70162We consider a self-similar fragmentation process in which the generic particle of size $x$ is replaced at probability rate $x^α$, by its offspring made of smaller particles, where $α$ 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 $t^{-1/α}$ and that the empirical distribution of sizes converges to a random limit which we characterise in terms of the reproduction law.17 pagesProbabilityMathematical Physics60J25, 60G18, 60J80text