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Williams’ decomposition of the Lévy continuum random tree and simultaneous extinction probability for populations with neutral mutations
We consider an initial Eve-population and a population of neutral mutants, such that the total population dies out in finite time. We describe the evolution of the Eve-population and the totalExpand
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A continuum-tree-valued Markov process
We present a construction of a Levy continuum random tree (CRT) associated with a super-critical continuous state branching process using the so-called exploration process and a Girsanov's theorem.Expand
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A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces
We present an extension of the Gromov-Hausdorff metric on the set of compact metric spaces: the Gromov-Hausdorff-Prokhorov metric on the set of compact metric spaces endowed with a finite measure. WeExpand
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Local limits of conditioned Galton-Watson trees: the condensation case
We  provide a complete picture of the local convergence of critical or subcritical Galton-Watson tree conditioned on having a large number of individuals with out-degree in a given set. The genericExpand
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Fragmentation associated with Lévy processes using snake
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 Le Gall-Le Jan and Duquesne-Le Gall,Expand
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Poisson Snake and Fragmentation
Our main object that we call the Poisson snake is a Brownian snake as introduced by Le Gall. This process has values which are trajectories of standard Poisson process stopped at some random finiteExpand
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Local limits of conditioned Galton-Watson trees: the infinite spine case
We give a necessary and sufficient condition for the convergence in distribution of a conditioned Galton-Watson tree to Kesten's tree. This yields elementary proofs of Kesten's result as well asExpand
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Record process on the Continuum Random Tree
By considering a continuous pruning procedure on Aldous's Brownian tree, we construct a random variablewhich is distributed, conditionally given the tree, according to the probability law introducedExpand
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The forest associated with the record process on a Lévy tree
We perform a pruning procedure on a Levy tree and instead of throwing away the removed sub-tree, we regraft it on a given branch (not related to the Levy tree). We prove that the tree constructed byExpand
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β-coalescents and stable Galton-Watson trees
Representation of coalescent processes using pruning of trees has been used by Goldschmidt and Martin for the Bolthausen-Sznitman coalescent and by Abraham and Delmas for the β(3/2, 1/2)-coalescent.Expand
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