A standard result in the theory of branching processes is that critical Galton-Watson processes can be classified in different universality classes according to the tail of their offspring distribution. The scaling limit of the genealogy of these processes depends on that universality class. When the offspring variance is finite genealogies are binary in the limit, whereas non-binary trees can emerge when the offspring distribution has heavy tail.
In this presentation, I will discuss extensions of these results to branching diffusions, which are branching processes with a spatial component. I will give a simple analytical criterion under which we expect the process to belong to the universality class of an alpha-stable continuous-state branching process. Interestingly, in the presence of space non-binary trees can now arise as the limit of processes with a bounded number of offspring. Finally, I will illustrate this criterion by studying the limit of the genealogy of a branching Brownian motion model introduced by Tourniaire (2021). This result proves a conjecture of Birzu, Hallatschek and Korolev (2018, 2021) in the so-called semi-pushed regime.
This is joint work with Julie Tourniaire and Emmanuel Schertzer
(University of Vienna).
