Electronic Journal of Probability

The Genealogy of Self-similar Fragmentations with Negative Index as a Continuum Random Tree

Bénédicte Haas and Grégory Miermont

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Abstract

We encode a certain class of stochastic fragmentation processes, namely self-similar fragmentation processes with a negative index of self-similarity, into a metric family tree which belongs to the family of Continuum Random Trees of Aldous. When the splitting times of the fragmentation are dense near 0, the tree can in turn be encoded into a continuous height function, just as the Brownian Continuum Random Tree is encoded in a normalized Brownian excursion. Under mild hypotheses, we then compute the Hausdorff dimensions of these trees, and the maximal Hölder exponents of the height functions.

Article information

Source
Electron. J. Probab. Volume 9 (2004), paper no. 4, 57-97.

Dates
Accepted: 9 February 2004
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465229690

Digital Object Identifier
doi:10.1214/EJP.v9-187

Mathematical Reviews number (MathSciNet)
MR2041829

Zentralblatt MATH identifier
1064.60076

Subjects
Primary: 60G18: Self-similar processes 60J25: Continuous-time Markov processes on general state spaces 60G09: Exchangeability

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Haas, Bénédicte; Miermont, Grégory. The Genealogy of Self-similar Fragmentations with Negative Index as a Continuum Random Tree. Electron. J. Probab. 9 (2004), paper no. 4, 57--97. doi:10.1214/EJP.v9-187. https://projecteuclid.org/euclid.ejp/1465229690


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