Orateur
Description
We consider the one-dimensional binary branching Brownian motion (BBM) and its fixed point problem. The recent work of Chen, Garban, and Shekhar (PTRF, 2023) classified the fixed points of BBM with the critical drift under the assumption that the fixed points have a top particle (i.e., a finite maximum particle) almost surely. A related result for supercritical drifts was obtained by Kabluchko (J. Appl. Prob., 2012), but under a more restrictive assumption of a locally finite intensity measure. We study the BBM with both critical and supercritical drifts and obtain a complete characterization of the fixed points without any additional assumptions. A key strategy in our analysis is the connection between BBM and the FKPP equation. This talk is based on joint work with Xinxin Chen, Atul Shekhar and Shuo Zhu.