Prof. Dr. Anton Bovier (Universität Bonn): The extremal process of branching Brownian motion.
Donnerstag, 11.10.2012 16:30 im Raum M5
Branching Brownian motion is a classical and canonical process in probability theory.
It is the simplest continuous time spatial branching process. A property of key interest is the structure of the process near its maximum for large times. This was first studies in the 70ies by McKeane, who discovered a deep connection to a classical reaction diffusion equation , the F-KPP equation. Bramson exploited these facts to reveal precise asysmptotics of the maximum of BBM. In this talk I present
some recent results obtained with Nicola Kistler and Louis-Pierre Arguin on the
full extremal process of BBM. In particular, we show that the extremal process of BBM converges to a new type of cluster point process. Moreover, we obtain an ergodic theorem showing that the time-average of the extremal proces of BBM converges almost surely to a random cluster point process. This proves and extends a conjecture by Lalley and Sellke form 1987.