Limiting distributions for the maximal displacement of branching Brownian motions

Yasuhito Nishimori; Yuichi Shiozawa

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arXiv · 1903.02851

Limiting distributions for the maximal displacement of branching Brownian motions

Yasuhito Nishimori·Yuichi Shiozawa

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Abstract

We determine the long time behavior and the exact order of the tail probability for the maximal displacement of a branching Brownian motion in Euclidean space in terms of the principal eigenvalue of the associated Schr\"odinger type operator. To establish our results, we show a sharp and locally uniform growth order of the Feynman-Kac semigroup.

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Yasuhito Nishimori, Yuichi Shiozawa. 2019-03-07. Limiting distributions for the maximal displacement of branching Brownian motions. https://arxiv.org/abs/1903.02851

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