Stein's method, heat kernel, and traces of powers of elements of compact Lie groups

Details Stein's method, heat kernel, and traces of powers of elements of compact Lie groups Stein's method, heat kernel, and traces of powers of elements of compact Lie groups

2010-05-07

arxiv.org/abs/1005.1306v1

Mathematics

Probability

17 pages

Scientific paper

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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