Stein's method, heat kernel, and linear functions on the orthogonal groups

DOI10.1016/J.JALGEBRA.2021.01.043arXiv1109.2975MaRDI QIDQ6227744

Publication date: 13 September 2011

Abstract: Combining Stein's method with heat kernel techniques, we study the function Tr(AO), where A is a fixed n by n real matrix over such that Tr(AA^t)=n, and O is 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 * squareroot(2) /(n-1), slightly improving the constant in a bound of Meckes, which was obtained by completely different methods.

Mathematics Subject Classification ID

Random matrices (algebraic aspects) (15B52) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Other matrix groups over fields (20H20) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

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