The size of random fragmentation intervals - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2008

The size of random fragmentation intervals


Two processes of random fragmentation of an interval are investigated. For each of them, there is a splitting probability at each step of the fragmentation process whose overall effect is to stabilize the global number of splitting events. More precisely, we consider two models. In the first model, the fragmentation stops which a probability $p$ witch can not depend on the fragment size. The number of stable fragments with sizes less than a given $t \geq 0$, denoted by $K(t)$, is introduced and studied. In the second one the probability to split a fragment of size $x$ is $p(x)=1-e^{-x}$. For this model we utilize the contraction method to show that the distribution of a suitably normalized version of the number of stable fragments converges in law. It's shown that the limit is the fixed-point solution (in the Wasserstein space) to a distributional equation. An explicit solution to the fixed-point equation is easily verified to be Gaussian.
Fichier principal
Vignette du fichier
dmAI0135.pdf (199.76 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive

Dates and versions

hal-01194669 , version 1 (07-09-2015)



Rafik Aguech. The size of random fragmentation intervals. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. pp.519-530, ⟨10.46298/dmtcs.3588⟩. ⟨hal-01194669⟩


96 View
636 Download



Gmail Facebook X LinkedIn More