Exponential approximation and Stein's method of exchangeable pairs

Jason Fulman, Nathan Ross

Published 2012-07-20Version 1

We derive a new result for exponential approximation using Stein's method of exchangeable pairs. As an application, an exponential limit theorem with error term is derived for |Tr(U)|^2, where Tr(U) denotes the trace of a matrix chosen from the Haar measure of the unitary group U(n,C).