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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.'
author:
- 'Bénédicte Haas[^1]  & Grégory Miermont[^2]'
title: 'The genealogy of self-similar fragmentations with negative index as a continuum random tree'
---

[**Key Words.** ]{}Self-similar fragmentation, continuum random tree, Hausdorff dimension, Hölder regularity.

[**A.M.S. Classification.** ]{}60G18, 60J25, 60G09.

Introduction
============

Self-similar fragmentation processes describe the evolution of an object that falls apart, so that different fragments keep on collapsing independently with a rate that depends on their sizes to a certain power, called the *index* of the self-similar fragmentation. A genealogy is naturally associated to such fragmentation processes, by saying that the common ancestor of two fragments is the block that included these fragments for 