论文标题
树指数随机步行的容量
Capacity of the range of tree-indexed random walk
论文作者
论文摘要
通过对无限的Galton-Watson工艺引入新的措施，并提供（离散）Green在树上的功能的估计，我们建立了关键分支随机步行能力的渐近行为：在高维度中，$ d \ ge 7 $，能力增长。在关键尺寸$ d = 6 $中，它与$ \ frac {n} {\ log n} $成正比成正比。
By introducing a new measure for the infinite Galton-Watson process and providing estimates for (discrete) Green's functions on trees, we establish the asymptotic behavior of the capacity of critical branching random walks: in high dimensions $d\ge 7$, the capacity grows linearly; and in the critical dimension $d=6$, it grows asymptotically proportional to $\frac{n}{\log n}$.
