期刊
JOURNAL OF ALGEBRA
卷 607, 期 -, 页码 272-285出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jalgebra.2021.01.043
关键词
Random matrix; Stein's method; Heat kernel
类别
资金
- Simons Grant [400528]
By combining Stein's method with heat kernel techniques, this study investigates the properties of the function Tr(AO), where A is a fixed matrix and O is sampled from the Haar measure of the orthogonal group. The research shows that the total variation distance between Tr(AO) and a standard normal random variable is bounded by a certain constant, slightly improving upon previous results obtained using different methods.
Combining Stein's method with heat kernel techniques, we study the function Tr(AO), where A is a fixed n x n matrix over R such that Tr(AA(t)) = n, and Ois from the Haar measure of the orthogonal group O(n, R). It is shown that the total variation distance of the random variable Tr(AO) to a standard normal random variable is bounded by 2 root 2/n-1, slightly improving the constant in a bound of Meckes, which was obtained by completely different methods. (c) 2021 Elsevier Inc. All rights reserved.
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