论文标题
限制具有随机光谱权重的总和分布
Limiting Distributions of Sums with Random Spectral Weights
论文作者
论文摘要
本文研究了$ z_n = \ sum_ {i = 1}^n a_i x_i $的加权总和的渐近性能，其中$ x_1，x_2，\ ldots，x_n $是i.i.d. Erdős-Rényi-Gilbert模型。特别是，我们证明了序列$ n^{ - 1} z_n $的中心极限型定理，并在$ x_1，x_2，\ ldots，x_n $上施加的不同条件。
This paper studies the asymptotic properties of weighted sums of the form $Z_n=\sum_{i=1}^n a_i X_i$, in which $X_1, X_2, \ldots, X_n$ are i.i.d.~random variables and $a_1, a_2, \ldots, a_n$ correspond to either eigenvalues or singular values in the classic Erdős-Rényi-Gilbert model. In particular, we prove central limit-type theorems for the sequences $n^{-1}Z_n$ with varying conditions imposed on $X_1, X_2, \ldots, X_n$.
