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arXiv · 2511.15647

A simpler path to Ergodic Theorems for the Frontier of Branching Brownian Motion

Gabriel Flath
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Abstract

We revisit the ergodic theorem for the frontier of branching Brownian motion (BBM). Motivated by the proof of Arguin, Bovier, and Kistler \cite{arguin2012ergodic}, we provide a shorter and more direct argument. It relies on two observations: pairs of extremal particles observed at well-separated times must have branched early, and pairs of early-branching extremal particles have negatively correlated positions. This yields the ergodic theorem for BBM and extends it to a broad class of functionals of the recentred maximum. We also address a gap in the path localization argument of \cite{arguin2012ergodic}.

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Gabriel Flath. 2025-11-19. A simpler path to Ergodic Theorems for the Frontier of Branching Brownian Motion. https://arxiv.org/abs/2511.15647

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