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

2011/09/13 by Jason Fulman, Fulman, Jason, Adrian Röllin +1 · 1 citation
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Geometry and complex manifolds #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1109.2975

openalex publication_date 2011/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Combining Stein's method with heat kernel techniques, we study the function\nTr(AO), where A is a fixed n by n real matrix over such that Tr(AA^t)=n, and O\nis from the Haar measure of the orthogonal group O(n,R). It is shown that the\ntotal variation distance of the random variable Tr(AO) to a standard normal\nrandom variable is bounded by 2 * squareroot(2) /(n-1), slightly improving the\nconstant in a bound of Meckes, which was obtained by completely different\nmethods.\n

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• Stein's method, Markov processes, and linear eigenvalue statistics of random matrices

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