AI 中文总结
本研究针对分支布朗运动导数鞅，建立几乎必然路径局部化结果，明确其极限由与极值粒子距离为s^(1/2)的细管内的粒子决定，刻画了贡献极限的粒子范围。
AI 中文摘要
分支布朗运动的前沿演化由导数鞅的极限决定，本研究明确了哪些粒子对该极限有贡献，精确建立了一个严格的几乎必然路径局部化结果，表明该极限由轨迹与极值粒子距离为s^(1/2)的细管内的粒子决定。
英文摘要
The evolution of the front of branching Brownian motion is determined by the limit of the derivative martingale. In this work, we characterise which particles contribute to this limit. Precisely, we establish a sharp almost sure path localisation result which shows that the limit is determined by those particles whose trajectory stays within a thin tube at distance $s^{1/2}$ from the extremal particle.
