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Stein’s method and characters of compact Lie groups. (English) Zbl 1186.60016

Summary: Stein’s method is used to study the trace of a random element from a compact Lie group or symmetric space. Central limit theorems are proved using very little information: character values on a single element and the decomposition of the square of the trace into irreducible components. This is illustrated for Lie groups of classical type and Dyson’s circular ensembles. The approach in this paper will be useful for the study of higher dimensional characters, where normal approximations need not hold.

MSC:

60F05 Central limit and other weak theorems
60C05 Combinatorial probability
22E30 Analysis on real and complex Lie groups
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