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Coalescence et fragmentation stochastiques, arbres aleatoires et processus de Levy

Abstract : We study certain stochastic processes involving either coalescence or fragmentation, with the help of random trees and Levy processes. We first describe the semigroup of a class of ordered fragmentations related to excursions of Levy processes with no positive jumps. These are in turn related to the so-called additive coalescent process. We provide negative results on the semigroup of certain fragmentations with a property called self-similarity, which has been introduced by Bertoin. Then, we study two "dual" devices for fragmenting the so-called continuum stable tree of Duquesne and Le Gall, giving rise to a pair of self-similar fragmentations, whose characteristics are entirely determined. We also encode the genealogy of self-similar fragmentations with negative index into continuum random trees. Last, we study the inhomogeneous continuum random trees of Aldous, Camarri and Pitman, obtained as a limit of random discrete p-trees. We describe the height and width processes of such trees as functionals of bridges with exchangeable increments. We also prove asymptotic results on p-mappings, which are formulated in terms of reflecting Brownian bridge, by connecting this model with the p-trees.
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Contributor : Gregory Miermont Connect in order to contact the contributor
Submitted on : Friday, December 19, 2003 - 2:26:16 PM
Last modification on : Thursday, December 10, 2020 - 10:52:45 AM
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  • HAL Id : tel-00004037, version 1


Gregory Miermont. Coalescence et fragmentation stochastiques, arbres aleatoires et processus de Levy. Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2003. English. ⟨tel-00004037⟩



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