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H 2 Martingales in self-similar growth-fragmentations and their applications

Auteurs : Bertoin, Jean (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : 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.

Codes MSC :
60G18 - Self-similar processes
60G44 - Martingales with continuous parameter
60G50 - Sums of independent random variables; random walks
60G51 - Processes with independent increments; Lévy processes
60J75 - Jump processes

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 23/06/2016
    Date de captation : 07/06/2016
    Collection : Probability and Statistics
    Sous collection : Research talks
    Domaine : Probability & Statistics
    Format : MP4 (.mp4) - HD
    Durée : 01:00:16
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2016-06-07_Bertoin.mp4

Informations sur la rencontre

Nom de la rencontre : Random trees and maps: probabilistic and combinatorial aspects / Arbres et cartes aléatoires : aspects probabilistes et combinatoires
Organisateurs de la rencontre : Haas, Bénédicte ; Goldschmidt, Christina ; Miermont, Grégory
Dates : 06/06/16 - 10/06/16
Année de la rencontre : 2016
URL Congrès : http://conferences.cirm-math.fr/1384.html

Citation Data

DOI : 10.24350/CIRM.V.18993003
Cite this video as: Bertoin, Jean (2016). Martingales in self-similar growth-fragmentations and their applications. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18993003
URI : http://dx.doi.org/10.24350/CIRM.V.18993003

Voir aussi

Bibliographie

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



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