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

Jason Fulman

Published 2010-05-07Version 1

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.