Oberseminar Stochastik

Arnab Chowdhury - Tata Institute of Fundamental Research-CAM, Bangalore -

FIXED POINTS AND HEAVY-TAILED EXTREME LEVEL SETS
OF BRANCHING BROWNIAN MOTION

In the first part of this talk, we discuss the fixed point problem of branching
Brownian motion (BBM). We establish a complete characterization of the fixed
points of BBM with critical and supercritical drifts under no additional assumptions
besides it being locally finite almost surely. In particular, we do not assume finite
intensity or the finite top particle conditions. We also give a full characterization of
the domain of attraction of the fixed points of BBM. The main idea is to use the
F-KPP equation together with the Bramson’s ψ-estimate to analyze the Laplace
functionals of BBM, and a finer analysis using a carefully designed Brownian thinning
technique. This part is based on a joint work with Xinxin Chen, Atul Shekhar and
Shuo Zhu.
In the second part, we turn to the extreme level sets of BBM. We show that these
level sets exhibit heavy-tailed behaviour, and we use this to establish a large-deviation
result for their growth.

Einladung