文章基本信息

标题：A universal error bound in the CLT for counting monochromatic edges in uniformly colored graphs
本地全文：下载
作者：Fang, Xiao
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2015
卷号：20
期号：0
页码：1-6
DOI：10.1214/ECP.v20-3707
语种：English
出版社：Electronic Communications in Probability
摘要：Let $\{G_n: n\geq 1\}$ be a sequence of simple graphs. Suppose $G_n$ has $m_n$ edges and each vertex of $G_n$ is colored independently and uniformly at random with $c_n$ colors. Recently, Bhattacharya, Diaconis and Mukherjee (2013) proved universal limit theorems for the number of monochromatic edges in $G_n$. Their proof was by the method of moments, and therefore was not able to produce rates of convergence. By a non-trivial application of Stein's method, we prove that there exists a universal error bound for their central limit theorem. The error bound depends only on $m_n$ and $c_n$, regardless of the graph structure.
关键词：Stein's method; normal approximation; rate of convergence; monochromatic edges;05C15; 60F05