Ergodicity of unitary random-matrix ensembles

Using Efetov's supersymmetry method, we prove the ergodicity of a wide class of unitary random-matrix ensembles. We do so by showing that the connected part of the autocorrelation function of any observable vanishes asymptotically. The essential elements of the proof consist in a polar decomposition of the saddle-point manifold, in the construction of the Efetov-Wegner terms generated in this way, and in an asymptotic expansion of these terms in inverse powers of the relevant parameter. (C) 2000 Academic Press.