Date/heure
6 mai 2021
10:45 - 11:45
Lieu
Teams
Oratrice ou orateur
Alex Watson (University College London)
Catégorie d'évènement Séminaire Probabilités et Statistique
Résumé
A growth-fragmentation is a stochastic process representing cells with continuously growing mass, which experience sudden splitting events. Growth-fragmentations are used to model cell division and protein polymerisation in biophysics. It is interesting to ask whether these processes converge toward an equilibrium, in which the number of cells is growing exponentially and the distribution of cell sizes approaches some fixed asymptotic profile. In this work, we study a process in which the growth and splitting of an individual cell is largely independent of its mass, with the exception that the mass is bounded above, so it cannot exceed a given constant. We give precise conditions to ensure that, almost surely, the process exhibits this equilibrium behaviour, and express the asymptotic profile in terms of an underlying Lévy process.
This is joint work with Emma Horton (Inria Bordeaux).