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Publications Influence

Williams’ decomposition of the Lévy continuum random tree and simultaneous extinction probability for populations with neutral mutations

- R. Abraham, J. Delmas
- Mathematics
- 11 April 2007

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 total… Expand

30 10- PDF

A continuum-tree-valued Markov process

- R. Abraham, J. Delmas
- Mathematics
- 27 April 2009

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

47 9- PDF

A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces

- R. Abraham, J. Delmas, Patrick Hoscheit
- Mathematics
- 24 February 2012

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. We… Expand

87 8- PDF

Local limits of conditioned Galton-Watson trees: the condensation case

- R. Abraham, J. Delmas
- Mathematics
- 26 November 2013

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 generic… Expand

23 6- PDF

Fragmentation associated with Lévy processes using snake

- R. Abraham, J. Delmas
- Mathematics
- 29 November 2005

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

33 6- PDF

Poisson Snake and Fragmentation

- R. Abraham, L. Serlet
- Mathematics
- 7 January 2002

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 finite… Expand

30 5- PDF

Local limits of conditioned Galton-Watson trees: the infinite spine case

- R. Abraham, J. Delmas
- Mathematics
- 15 April 2013

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 as… Expand

41 4- PDF

Record process on the Continuum Random Tree

- R. Abraham, J. Delmas
- Mathematics
- 19 July 2011

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 introduced… Expand

20 4- PDF

The forest associated with the record process on a Lévy tree

- R. Abraham, J. Delmas
- Mathematics
- 11 April 2012

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 by… Expand

20 3- PDF

β-coalescents and stable Galton-Watson trees

- R. Abraham, J. Delmas
- 2013

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

14 3- PDF

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