Mon, 24 Jan 2005
14:15
14:15
DH 3rd floor SR
The genealogy of self-similar fragmentations with a negative index as a continuum random tree
Dr Benedict Haas
(Department of Statistics, Oxford)
Abstract
Fragmentation processes model the evolution of a particle that split as time goes on. When small particles split fast enough, the fragmentation is intensive and the initial mass is reduced to dust in finite time. We encode such fragmentation into a continuum random tree (CRT) in the sense of Aldous. When the splitting times are dense near 0, the fragmentation CRT is in turn encoded into a continuous (height) function. Under some mild hypotheses, we calculate the Hausdorff dimension of the CRT, as well as the maximal H