Abstracts > Angtuncio Hernández Osvaldo

Joint work with David Clancy Jr.

One of the most widely used models to describe population evolution is the Bienaymé--Galton--Watson tree. In the 1990s, Aldous demonstrated that, under certain hypotheses, by conditioning these trees to have a fixed size and allowing this size to tend to infinity, the limit obtained is a compact metric space known as the Continuum Random Tree. In this talk, we present a generalization of this result to the case of multitype Bienaymé--Galton--Watson trees conditioned to be large. In this model, individuals of different types coexist, and their reproduction law depends precisely on their specific type. We will show how, under appropriate conditions, the limit can be described as a compact metric space that we term the multitype Lévy tree. Our technique is the first in which the limiting object preserves its multitype structure. The methodologies employed rely on the convergence of marked measured metric spaces, an iterative ``gluing'' procedure of these spaces, and the use of spectrally positive Lévy additive fields to code the trees.