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 Schrödinger type operator. To establish our results, we show a sharp and locally uniform growth order of the Feynman–Kac semigroup.
The second author was supported in part by JSPS KAKENHI No. JP17K05299.
"Limiting distributions for the maximal displacement of branching Brownian motions." J. Math. Soc. Japan 74 (1) 177 - 216, January, 2022. https://doi.org/10.2969/jmsj/85158515