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

Probability 2022-06-17 v1

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 ξ=(ξ(x))xR\xi = \left(\xi(x)\right)_{x\in\mathbb{R}} satisfying certain conditions. We show that the maximum position MtM_t of particles alive at time tt satisfies a quenched strong law of large numbers and an annealed invariance principle.

Keywords

Cite

@article{arxiv.2206.07950,
  title  = {Invariance principle for the maximal position process of branching Brownian motion in random environment},
  author = {Haojie Hou and Yan-Xia Ren and Renming Song},
  journal= {arXiv preprint arXiv:2206.07950},
  year   = {2022}
}