论文标题
三角形阵列上不完整的U统计量的中心限制定理
A Central Limit Theorem for incomplete U-statistics over triangular arrays
论文作者
论文摘要
我们分析了独立随机变量的三角形阵列上不完整的$ U $统计量的波动。我们给出了中心限制定理（CLT，简称CLT）的标准，从而证明了u统计量的适当缩放和中心版本会收敛到正常的随机变量。我们的证明方法依赖于Martingale CLT。可能的应用程序 - 将在随机图上随机步行的撞击时间 - 将在\ cite {lote20b}中介绍
We analyze the fluctuations of incomplete $U$-statistics over a triangular array of independent random variables. We give criteria for a Central Limit Theorem (CLT, for short) to hold in the sense that we prove that an appropriately scaled and centered version of the U-statistic converges to a normal random variable. Our method of proof relies on a martingale CLT. A possible application -- a CLT for the hitting time for random walk on random graphs -- will be presented in \cite{LoTe20b}
