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arXiv · 2206.07950

Invariance principle for the maximal position process of branching Brownian motion in random environment

Haojie Hou·Yan-Xia Ren·Renming Song
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Abstract

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 $\xi = \left(\xi(x)\right)_{x\in\mathbb{R}}$ 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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Haojie Hou, Yan-Xia Ren, Renming Song. 2022-06-16. Invariance principle for the maximal position process of branching Brownian motion in random environment. https://arxiv.org/abs/2206.07950

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