Open Access
2013 General fragmentation trees
Robin Stephenson
Author Affiliations +
Electron. J. Probab. 18: 1-45 (2013). DOI: 10.1214/EJP.v18-2703


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.


Download Citation

Robin Stephenson. "General fragmentation trees." Electron. J. Probab. 18 1 - 45, 2013.


Accepted: 24 November 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1297.60023
MathSciNet: MR3141802
Digital Object Identifier: 10.1214/EJP.v18-2703

Keywords: continuum random trees , fragmentation trees , Self-similar fragmentations

Vol.18 • 2013
Back to Top