Compensated fragmentation processes and limits of dilated fragmentations

Abstract

A new class of fragmentation-type random processes is introduced, in which, roughly speaking, the accumulation of small dislocations which would instantaneously shatter the mass into dust, is compensated by an adequate dilation of the components. An important feature of these compensated fragmentations is that the dislocation measure $\nu$ which governs their evolutions has only to fulfill the integral condition $\int_{\mathit{p}}$ (1-$\mathit{p}{1}$)$^{2}\nu$(d$\mathbf{p}$ < $\infty$, where $\mathbf{p}$ = ($\mathit{p}{1}$ Show more