On two fragmentation schemes with algebraic splitting probability
Volume 33 / 2006
Abstract
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.
