AI 中文总结
该研究针对多维分支布朗运动，通过分析其前沿时间平均对应的临界导数鞅性质，证明该函数无处局部有界，进而得出分支布朗运动存在强持续各向异性的结论。
AI 中文摘要
我们研究多维分支布朗运动（BBM）前沿的角度变化。该前沿的时间平均与临界导数鞅的长时间极限相关，后者是球面上的随机可积函数。我们证明该函数无处局部有界，由此得出BBM呈现强持续各向异性：不同方向的BBM前沿之间存在密集且任意大的间隙。
英文摘要
We study angular variation in the frontier of branching Brownian motion (BBM) in multiple dimensions. The time average of this frontier is tied to the long-time limit of the critical derivative martingale, which is a random integrable function on the sphere. We show that this function is nowhere locally bounded. As a consequence, BBM exhibits strong persistent anisotropy: there are dense arbitrarily large gaps between the BBM frontier in different directions.
Comments44 pages
