论文标题
关键分支随机步行范围的法律收敛
Convergence in law for the capacity of the range of a critical branching random walk
论文作者
论文摘要
令$ r_n $为$ \ mathbb z^d $上的$ n $粒子的关键分支随机步行的范围，这是由关键的加尔顿（Wallton-Watson Tree）访问的一组站点，其随机步行索引，其条件是恰好拥有$ n $ dertices。对于$ d \ in \ {3，4，5 \} $，我们证明$ n^{ - \ frac {d-2} 4} \ mathtt {cap}^{（d）}（d）}（r_n）$，$ r_n $的重新性化能力，以$ r_n $的方式为法律，以支持集成的Super-Super-Super-Super-super-Brownian Ixcours Increstion。证明依赖于对关键分支随机步行与$ \ Mathbb z^d $的独立简单随机步行之间的交叉概率的研究。
Let $R_n$ be the range of a critical branching random walk with $n$ particles on $\mathbb Z^d$, which is the set of sites visited by a random walk indexed by a critical Galton--Watson tree conditioned on having exactly $n$ vertices. For $d\in\{3, 4, 5\}$, we prove that $n^{-\frac{d-2}4} \mathtt{cap}^{(d)}(R_n)$, the renormalized capacity of $R_n$, converges in law to the capacity of the support of the integrated super-Brownian excursion. The proof relies on a study of the intersection probabilities between the critical branching random walk and an independent simple random walk on $\mathbb Z^d$.
