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2012 Stein's method, heat kernel, and traces of powers of elements of compact Lie groups
Jason Fulman
Author Affiliations +
Electron. J. Probab. 17: 1-16 (2012). DOI: 10.1214/EJP.v17-2251

Abstract

Combining Stein's method with heat kernel techniques, we show that the trace of the $j$th power of an element of $U(n,\mathbb{C}), USp(n,\mathbb{C})$, or $SO(n,\mathbb{R})$ has a normal limit with error term $C \dot j/n$, with $C$ an absolute constant. In contrast to previous works, here $j$ may be growing with $n$. The technique might prove useful in the study of the value distribution of approximate eigenfunctions of Laplacians.

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Jason Fulman. "Stein's method, heat kernel, and traces of powers of elements of compact Lie groups." Electron. J. Probab. 17 1 - 16, 2012. https://doi.org/10.1214/EJP.v17-2251

Information

Accepted: 18 August 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1252.60012
MathSciNet: MR2968673
Digital Object Identifier: 10.1214/EJP.v17-2251

Subjects:
Primary: 60B20
Secondary: 15B52, 60F05

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