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## On two fragmentation schemes with algebraic splitting probability

### Tom 33 / 2006

Applicationes Mathematicae 33 (2006), 95-110 MSC: Primary 60G57, 62E17; Secondary 60K99, 62E15, 62E20. DOI: 10.4064/am33-1-8

#### Streszczenie

Consider the following inhomogeneous fragmentation model: suppose an initial particle with mass $x_{0}\in (0,1)$ undergoes splitting into $b>1$ fragments of random sizes with some size-dependent probability $p(x_{0})$. With probability $1-p(x_{0})$, this particle is left unchanged forever. Iterate the splitting procedure on each sub-fragment if any, independently. Two cases are considered: the stable and unstable case with $p( x_{0}) =x_{0}^{a}$ and $p(x_{0}) =1-x_{0}^{a}$ respectively, for some $a>0.$ In the first (resp. second) case, since smaller fragments split with smaller (resp. larger) probability, one suspects some stabilization (resp. instability) of the fragmentation process. Some statistical features are studied in each case, chiefly fragment size distribution, partition function, and the structure of the underlying random fragmentation tree.

#### Autorzy

• M. GhorbelLaboratoire de Physique Théorique et Modélisation
CNRS-UMR 8089 et Université de Cergy-Pontoise
2 Avenue Adolphe Chauvin
95032 Cergy-Pontoise, France
and
Laboratoire d' Analyse, Géometrie et Applications
CNRS-UMR 7539, Institut Galilée
Université de Paris 13
93340 Villetaneuse, France
e-mail
• T. HuilletLaboratoire de Physique Théorique et Modélisation
CNRS-UMR 8089 et Université de Cergy-Pontoise
2 Avenue Adolphe Chauvin
95032 Cergy-Pontoise, France
e-mail

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