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Invariance principle for the maximal position process of branching Brownian motion in random environment
Haojie Hou, Yan-Xia Ren, Renming Song · 2022-06-16 · via math.PR updates on arXiv.org

In this paper we study the maximal position process of branching Brownian motion in random spatial environment. The random environment is given by a process $ξ= \left(ξ(x)\right)_{x\in\mathbb{R}}$ satisfying certain conditions. We show that the maximum position $M_t$ of particles alive at time $t$ satisfies a quenched strong law of large numbers and an annealed invariance principle.

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