On two fragmentation schemes with algebraic splitting probability

M. Ghorbel, and T. Huillet. "On two fragmentation schemes with algebraic splitting probability." Applicationes Mathematicae 33.1 (2006): 95-110. <http://eudml.org/doc/279026>.

@article{M2006,
abstract = {Consider the following inhomogeneous fragmentation model: suppose an initial particle with mass x₀ ∈ (0,1) undergoes splitting into b > 1 fragments of random sizes with some size-dependent probability p(x₀). With probability 1-p(x₀), 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 $p(x₀) = x₀^\{a\}$ and $p(x₀) = 1-x₀^\{a\}$ 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.},
author = {M. Ghorbel, T. Huillet},
journal = {Applicationes Mathematicae},
keywords = {fragmentation models; random fragmentation tree; random particles; partition function},
language = {eng},
number = {1},
pages = {95-110},
title = {On two fragmentation schemes with algebraic splitting probability},
url = {http://eudml.org/doc/279026},
volume = {33},
year = {2006},
}

TY - JOUR
AU - M. Ghorbel
AU - T. Huillet
TI - On two fragmentation schemes with algebraic splitting probability
JO - Applicationes Mathematicae
PY - 2006
VL - 33
IS - 1
SP - 95
EP - 110
AB - Consider the following inhomogeneous fragmentation model: suppose an initial particle with mass x₀ ∈ (0,1) undergoes splitting into b > 1 fragments of random sizes with some size-dependent probability p(x₀). With probability 1-p(x₀), 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 $p(x₀) = x₀^{a}$ and $p(x₀) = 1-x₀^{a}$ 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.
LA - eng
KW - fragmentation models; random fragmentation tree; random particles; partition function
UR - http://eudml.org/doc/279026
ER -