The fixed points of Branching Brownian Motion

Abstract

In this work, we characterize all the point processes $\theta ={\sum }_{i\in \mathbb{N}}{\delta }_{x_i}$ on $\mathbb{R}$ which are left invariant under branching Brownian motions with critical drift $-\sqrt{2}$. Our characterization holds under the only assumption that $\theta ({\mathbb{R}}_{+})<\infty$ almost surely.

34 pages, 2 figures