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
Combining Stein's method with heat kernel techniques, we show that the trace of the $j$th power of an element of $U(n,\mathbb{C}), USp(n,\mathbb{C})$, or $SO(n,\mathbb{R})$ has a normal limit with error term $C \dot j/n$, with $C$ an absolute constant. In contrast to previous works, here $j$ may be growing with …