Upper moderate deviation probabilities for the maximum of branching Brownian motion

2025/05/16 by Chataignier, Louis · 1 citation
#60F10 #60J80 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2505.11363

Abstract

It is known from Bramson (1983) that the maximum of branching Brownian motion at time t is asymptotically around an explicit function m_t, which involves a first ballistic order and a logarithmic correction. In this paper, we give an asymptotic equivalent for its upper moderate deviation probability, that is, the probability that the maximum achieves m_t + x_t at time t, where 1 ≪ x_t ≪ t. We adopt a probabilistic approach that employs a modified version of the second moment method. As a byproduct, we obtain information about the typical behavior of particles contributing to such deviations.

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