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Martingales in self-similar growth-fragmentations and their applications

De Jean Bertoin

Apparaît dans la collection : Random trees and maps: probabilistic and combinatorial aspects / Arbres et cartes aléatoires : aspects probabilistes et combinatoires

This talk is based on a work jointly with Timothy Budd (Copenhagen), Nicolas Curien (Orsay) and Igor Kortchemski (Ecole Polytechnique). Consider a self-similar Markov process $X$ on $[0,\infty)$ which converges at infinity a.s. We interpret $X(t)$ as the size of a typical cell at time $t$, and each negative jump as a birth event. More precisely, if ${\Delta}X(s) = -y < 0$, then $s$ is the birth at time of a daughter cell with size $y$ which then evolves independently and according to the same dynamics. In turn, daughter cells give birth to granddaughter cells each time they make a negative jump, and so on. The genealogical structure of the cell population can be described in terms of a branching random walk, and this gives rise to remarkable martingales. We analyze traces of these mar- tingales in physical time, and point at some applications for self-similar growth-fragmentation processes and for planar random maps.

Informations sur la vidéo

Données de citation

  • DOI 10.24350/CIRM.V.18993003
  • Citer cette vidéo Bertoin, Jean (07/06/2016). Martingales in self-similar growth-fragmentations and their applications. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18993003
  • URL https://dx.doi.org/10.24350/CIRM.V.18993003

Bibliographie

  • Bertoin, J., Budd, T., Curien, N., & Kortchemski, I. (2016). Martingales in self-similar growth-fragmentations and their connections with random planar maps. <arXiv:1605.00581> - https://arxiv.org/abs/1605.00581

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