208 citations
- Centre National de la Recherche ScientifiqueFR5 papers
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- Laboratoire de Physique ThéoriqueFR3 papers
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5 papers · 1 filter
The Hausdorff measure of stable trees
Thomas Duquesne, Jean-Francois Le Gall
We study fine properties of the so-called stable trees, which are the scaling limits of critical Galton-Watson trees conditioned to be large. In particular we derive the exact Haus…
Probabilistic and fractal aspects of Levy trees
Thomas Duquesne, Jean-Francois Le Gall
We investigate the random continuous trees called Lévy trees, which are obtained as scaling limits of discrete Galton-Watson trees. We give a mathematically precise definition of t…
Conditioned Brownian trees
Jean-Francois Le Gall, Mathilde Weill
We consider a Brownian tree consisting of a collection of one-dimensional Brownian paths started from the origin, whose genealogical structure is given by the Continuum Random Tree…
Self-similar fragmentations derived from the stable tree II: splitting at nodes
Gregory Marc Miermont
We study a natural fragmentation process of the so-called stable tree introduced by Duquesne and Le Gall, which consists in removing the nodes of the tree according to a certain pr…
The exploration process of inhomogeneous continuum random trees, and an extension of Jeulin's local time identity
David J Aldous, Gregory Miermont, Jim Pitman
We study the inhomogeneous continuum random trees (ICRT) that arise as weak limits of birthday trees. We give a description of the exploration process, a function defined on [0,1]…