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Self-similar growth-fragmentation models

Banff International Research Station for Mathematical Innovation and Discovery

We look at models of fragmentation with growth. In such a model, one has a number of independent cells, each of which grows continuously in time until a fragmentation event occurs, at which point the cell splits into two child cells of a smaller mass. Each of the children is independent and behaves in the same way as its parent. The rate of fragmentation is self-similar, that is, the rate at which each cell splits is a power of the mass. This is a random model; looking at its mean-field behaviour gives the growth-fragmentation equation, which is a deterministic PDE. We describe probabilistic solutions to the equation, using growth-fragmentations and positive self-similar Markov processes. In certain cases, we see spontaneous generation of positive solutions from zero initial mass. Based on joint work with Jean Bertoin (University of Zurich).

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

video/mp4

Author affiliation: University of Manchester

2017-06-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/62016

Unreviewed

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