461 citations
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7 papers · 2 filters
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…
Random Trees, Levy Processes and Spatial Branching Processes
Thomas Duquesne, Jean-Francois Le Gall
We investigate the genealogical structure of general critical or subcritical continuous-state branching processes. Analogously to the coding of a discrete tree by its contour funct…
Equilibrium for fragmentation with immigration
Benedicte Haas
This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a…
Equivalent and absolutely continuous measure changes for jump-diffusion processes
Patrick Cheridito, Damir Filipovic, Marc Yor
We provide explicit sufficient conditions for absolute continuity and equivalence between the distributions of two jump-diffusion processes that can explode and be killed by a pote…
Continuous and Tractable models for the Variation of Evolutionary Rates
Thomas Lepage, Stephan Lawi, Paul Tupper +1
We propose a continuous model for evolutionary rate variation across sites and over the tree and derive exact transition probabilities under this model. Changes in rate are modelle…
A probabilistic approach to the geometry of the \ell_p^n-ball
Franck Barthe, Olivier Guedon, Shahar Mendelson +1
This article investigates, by probabilistic methods, various geometric questions on B_p^n, the unit ball of \ell_p^n. We propose realizations in terms of independent random variabl…