Probability Seminar
Thursday, March 19, 2009, 4:15pm, 119 Physics
Lea Popovic (Concordia)
Genealogy of Catalytic Populations
Abstract:- For neutral branching models of two types of populations there are
three universality classes of behavior: independent branching,
(one-sided) catalytic branching and mutually catalytic branching. Loss
of independence in the two latter models generates many new features
in the way that the populations evolve.
In this talk I will focus on describing the genealogy of a catalytic
branching diffusion. This is the many individual fast branching limit
of an interacting branching particle model involving two populations,
in which one population, the "catalyst", evolves autonomously
according to a Galton-Watson process while the other population, the
"reactant", evolves according to a branching dynamics that is
dependent on the number of catalyst particles.
We show that the sequence of suitably rescaled family forests for the
catalyst and reactant populations converge in Gromov-Hausdorff
topology to limiting real forests. We characterize their distribution
via a reflecting diffusion and a collection of point-processes. We
compare geometric properties and statistics of the catalytic branching
forests with those of the "classical" (independent branching) forest.
This is joint work with Andreas Greven and Anita Winter. [video]
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