Open Collections

Local explosion in growth-fragmentation processes

Banff International Research Station for Mathematical Innovation and Discovery

Growth-fragmentation processes describe a family of particles which can grow larger or smaller with time, and occasionally split in a conservative manner. In the self-similar case, it is known that a simple Malthusian condition ensures that the process does not locally explode, in the sense that for all times, the masses of all the particles can be listed in non-increasing order. We shall present here the converse: when this Malthusian condition is not verified, then the growth-fragmentation process explodes almost surely. Our proof involves using the additive martingale to bias the probability measure and obtain a spine decomposition of the process, as well as properties of self-similar Markov processes. Based on a joint work with Robin Stephenson.

Mathematics; Probability theory and stochastic processes; Functional analysis; Probability / statistical mechanics

video/mp4

Author affiliation: Universität Zürich

2017-06-19

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/62024

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/