Variable speed branching Brownian motion 1. Extremal processes in the weak correlation regime

Anton Bovier; Lisa Hartung

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arXiv · 1403.6332

Variable speed branching Brownian motion 1. Extremal processes in the weak correlation regime

Anton Bovier·Lisa Hartung

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Abstract

We prove the convergence of the extremal processes for variable speed branching Brownian motions where the "speed functions", that describe the time-inhomogeneous variance, lie strictly below their concave hull and satisfy a certain weak regularity condition. These limiting objects are universal in the sense that they only depend on the slope of the speed function at $0$ and the final time $t$. The proof is based on previous results for two-speed BBM obtained in a recent paper of ours and uses Gaussian comparison arguments to extend these to the general case.

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Anton Bovier, Lisa Hartung. 2014-03-25. Variable speed branching Brownian motion 1. Extremal processes in the weak correlation regime. https://arxiv.org/abs/1403.6332

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