General Fragmentation Trees
Probability
2013-04-02 v2
Abstract
We show that the genealogy of any self-similar fragmentation process can be encoded in a compact measured real tree. Under some Malthusian hypotheses, we compute the fractal Hausdorff dimension of this tree through the use of a natural measure on the set of its leaves. This generalizes previous work of Haas and Miermont which was restricted to conservative fragmentation processes.
Cite
@article{arxiv.1303.6873,
title = {General Fragmentation Trees},
author = {Robin Stephenson},
journal= {arXiv preprint arXiv:1303.6873},
year = {2013}
}