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arXiv · 1109.2975

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

Jason Fulman·Adrian Röllin
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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.

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Jason Fulman, Adrian Röllin. 2011-09-14. Stein's method, heat kernel, and linear functions on the orthogonal groups. https://arxiv.org/abs/1109.2975

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