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In this review, we investigate a key information-theoretic performance metricin multiple-antenna wireless communications, the so-called outage probability.This quantity may be expressed in terms of a moment generating function, forwhich we present two separate integral representations, one involving aparticular $\sigma$-form of Painlev\'e V. We also present a representationinvolving a non-linear second order difference equation.

Perturbed Laguerre Unitary Ensembles, Painlev\'e V and Information Theory