Ergodicity of random-matrix theories: The unitary case

We prove ergodicity of unitary random-matrix theories by showing that the a utocorrelation function with respect to energy or magnetic field strength o f any observable vanishes asymptotically. We do so using Efetov's supersymm etry method, a polar decomposition of the saddle-point manifold, and an asy mptotic evaluation of the boundary terms generated in this fashion.