181 citations
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5 papers · 2 filters
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…
Continuum tree limit for the range of random walks on regular trees
Thomas Duquesne
Let be an integer greater than 1 and let $W^{\ee}=(W^{\ee}_n; n\geq 0)$ be a random walk on the -ary rooted tree $\U_b$, starting at the root, going up (resp. down) with pro…
Growth of Levy trees
Thomas Duquesne, Matthias Winkel
We construct random locally compact real trees called Levy trees that are the genealogical trees associated with continuous-state branching processes. More precisely, we define a g…
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…
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…