论文标题
关于在随机环境中最大的布朗运动的最大紧密度
On the tightness of the maximum of branching Brownian motion in random environment
论文作者
论文摘要
我们考虑在空间随机的分支环境（BBMRE）中考虑一维的布朗运动，并表明，对于几乎每个实现环境的实现，BBMRE的最大粒子的分布在其中位数围绕其中位数重新中心的分布会随着时间的变化而紧密。该结果与以下事实形成了鲜明的对比：解决方案的过渡方面 - Kolmogorov--petrovskii-piskunov（F-KPP）方程，通常在时间上并不统一。特别是，这强调了 - 与均质环境中的均匀分支布朗运动和F-KPP方程的设置相比，引入随机环境会导致更复杂的行为。
We consider one-dimensional branching Brownian motion in spatially random branching environment (BBMRE) and show that for almost every realisation of the environment, the distributions of the maximal particle of the BBMRE re-centred around its median are tight as time evolves. This result is in stark contrast to the fact that the transition fronts in the solution to the randomised Fisher--Kolmogorov--Petrovskii--Piskunov (F-KPP) equation are, in general, not bounded uniformly in time. In particular, this highlights that -- when compared to the settings of homogeneous branching Brownian motion and the F-KPP equation in a homogeneous environment -- the introduction of a random environment leads to a much more intricate behaviour.
