Talk by Jean-François Delmas (Ecole Nationale des Ponts et Chaussées, visiting UCSD)
Date and Time: Thursday, April 20, 2006, 10:00 AM in AP&M 6218.
Title: Fragmentation of the continuous random tree.
Abstract:
We consider the height process of a Lévy process with no negative jumps,
and its associated continuous tree representation. Using Lévy snake
tools developed by Duquesne and Le Gall, we construct a fragmentation
process (at node and at height), which in the stable case corresponds to
the self-similar fragmentation (at node and at height) described by
Miermont. For the general fragmentation process we compute a family of
dislocation measures. We compute also the asymptotic for the number of
small fragments at time t. In the case of the fragmentation at node,
this limit is increasing in t and discontinuous. In the alpha-stable
case the fragmentation is self-similar and the results are close (but
still different) to those obtained by Bertoin for general self-similar
fragmentations under a strong additional assumtion which is not
fulfilled here.