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

摘要

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?C j, 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.