Skip to Main content Skip to Navigation
Conference papers

The size of random fragmentation intervals

Abstract : 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.
Complete list of metadata

Cited literature [17 references]  Display  Hide  Download

https://hal.inria.fr/hal-01194669
Contributor : Coordination Episciences Iam <>
Submitted on : Monday, September 7, 2015 - 12:50:52 PM
Last modification on : Thursday, October 22, 2020 - 2:28:02 PM
Long-term archiving on: : Tuesday, December 8, 2015 - 12:54:43 PM

File

dmAI0135.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01194669, version 1

Collections

Citation

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

Share

Metrics

Record views

176

Files downloads

748