Abstract: 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,∞) 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 ΔX(s)=−y [is less than] 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.
Recording during the thematic meeting : "Random trees and maps: probabilistic and combinatorial aspects" the June 7, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
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Jean Bertoin: Martingales in self-similar growth-fragmentations and their applications cnrs montpellier | |
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| Science & Technology | Upload TimePublished on 29 Jun 2016 |
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