Stein’s Method and Characters of Compact Lie Groups
نویسنده
چکیده
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.
منابع مشابه
Stein’s Method, Heat Kernel, and Traces of Powers of Elements of Compact Lie Groups
Combining Stein’s method with heat kernel techniques, we show that the trace of the jth power of an element of U(n, C), USp(n, C) or SO(n, R) has a normal limit with error term of order j/n. In contrast to previous works, here j may be growing with n. The technique should prove useful in the study of the value distribution of approximate eigenfunctions of Laplacians.
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[1] Hare, Kathryn E., Wilson, David C., and Yee, Wai Ling, Pointwise Estimates of the Size of Characters of Compact Lie Groups, Journal of the Australian Mathematics Society Series A 69 (2000), no. 1, 61–84. [2] Hare, Kathryn E. and Yee, Wai Ling, The Singularity of Orbital Measures on Compact Lie Groups, Revista Math. Iberoamericana 20 (2004), no. 2, 517–530. Broadly, this research could be de...
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