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arXiv · 2409.16104

Branching brownian motion conditioned on large level sets

Xinxin Chen·Heng Ma
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Abstract

We study the precise large deviation probabilities for the sizes of intermediate level sets in branching Brownian motion (BBM). Our conclusions improve a result of A\"{i}dekon, Hu and Shi in [J. Math. Sci. \textbf{238}(2019)]. Additionally, we analyze the typical behaviors of BBM conditioned on large level sets. Our approach relies on the connections between intermediate level sets, additive martingale limits of BBM, and the global minimum of linearly transformed BBMs.

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Xinxin Chen, Heng Ma. 2024-09-24. Branching brownian motion conditioned on large level sets. https://arxiv.org/abs/2409.16104

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