We consider the model of branching Brownian motion with a single catalytic point at the origin and binary branching. We establish some fine results for the asymptotic behaviour of the numbers of particles travelling at different speeds and in particular prove that the point process of particles travelling at the critical speed converges in distribution to a mixture of Poisson point processes.

中文翻译：

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催化分支布朗运动中边界附近颗粒的极限分布

我们考虑在原点和单个分支处具有单个催化点的布朗运动分支模型。我们为以不同速度传播的粒子数目的渐近行为建立了一些很好的结果，特别是证明了以临界速度传播的粒子的点过程收敛于分布到泊松点过程的混合。