# 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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-00605146
Contributor : Piotr Graczyk <>
Submitted on : Thursday, June 30, 2011 - 4:58:40 PM
Last modification on : Monday, March 9, 2020 - 6:15:52 PM
Document(s) archivé(s) le : Saturday, October 1, 2011 - 2:26:50 AM

### Files

GraczykIshiSENT.pdf
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### Identifiers

• HAL Id : hal-00605146, version 1
• ARXIV : 1107.0147

### Citation

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

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