APPLICATIONS OF THE DOTSENKO-FATEEV INTEGRAL IN RANDOM-MATRIX MODELS

The characteristic multi-dimensional integrals that represent physical quantities in random-matrix models, when calculated within the supers ymmetry method, can be related to a class of integrals introduced in t he context of two-dimensional conformal field theories by Dotsenko and Fateev. Known results on these Dotsenko-Fateev integrals provide a me ans by which to perform explicit calculations (otherwise difficult) in random-matrix theory. We illustrate this by (i) an evaluation of the mean squared S-matrix elements for the Gaussian orthogonal ensemble co upled with M external channels, and (ii) a direct derivation of the as ymptotic behaviour of the dynamical density-density correlator in the limit of large spatial and temporal separation for the Calogero-Suther land model which, at certain couplings, is known to map onto the param eter-dependent random-matrix ensembles.