The genealogy of self-similar fragmentations with negative index as a continuum random tree

We encode a certain class of stochastic fragmentation processes,namely self-similar fragmentation processes with a negative indexof self-similarity, into a metric family tree which belongs to thefamily of Continuum Random Trees of Aldous. When the splittingtimes of the fragmentation are dense near 0, the tree can in turnbe encoded into a continuous height function, just as the BrownianContinuum Random Tree is encoded in a normalized Brownianexcursion. Under mild hypotheses, we then compute the Hausdorffdimensions of these trees, and the maximal Hölder exponents ofthe height functions