An invariance principle for branching diffusions in bounded domains

Vortrag von Dr. Ellen Powell

Datum: 25.10.17  Zeit: 17.15 - 18.15  Raum: ETH HG G 43

I will discuss branching diffusions in a bounded domain D of R^d, in which particles are killed upon hitting the boundary. It is known that such a process undergoes a phase transition when the branching rate exceeds a critical value: a multiple of the first eigenvalue of the diffusion. The main focus of this talk will be the genealogical tree associated with the critical process, when it is conditioned to survive. I will prove that this converges to Aldous' Continuum Random Tree under appropriate rescaling.