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Preprints, Working Papers, ... Year : 2011

Riesz measures and Wishart laws associated to quadratic maps

Abstract

We introduce a natural definition of Riesz measures and Wishart laws associated to an $\Omega$-positive (virtual) quadratic map, where $\Omega \subset \real^n$ is a regular open convex cone. We give a general formula for moments of the Wishart laws. Moreover, if the quadratic map has an equivariance property under the action of a linear group acting on the cone $\Omega$ transitively, then the associated Riesz measure and Wishart law are described explicitly by making use of theory of relatively invariant distributions on homogeneous cones.
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Dates and versions

hal-00605146 , version 1 (30-06-2011)

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Piotr Graczyk, Ishi Hideyuki. Riesz measures and Wishart laws associated to quadratic maps. 2011. ⟨hal-00605146⟩
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