# Ewens measures on compact groups and hypergeometric kernels

Abstract : On unitary compact groups the decomposition of a generic element into product of reflections induces a decomposition of the characteristic polynomial into a product of factors. When the group is equipped with the Haar probability measure, these factors become independent random variables with explicit distributions. Beyond the known results on the orthogonal and unitary groups (O(n) and U(n)), we treat the symplectic case. In U(n), this induces a family of probability changes analogous to the biassing in the Ewens sampling formula known for the symmetric group. Then we study the spectral properties of these measures, connected to the pure Fisher-Hartvig symbol on the unit circle. The associated orthogonal polynomials give rise, as $n$ tends to infinity to a limit kernel at the singularity.
Type de document :
Communication dans un congrès
Séminaire de Probabilités XLIII, 2009, France. 2006, pp.351-377, 2011, 〈10.1007/978-3-642-15217-7〉
Domaine :

https://hal.archives-ouvertes.fr/hal-00690322
Soumis le : lundi 23 avril 2012 - 10:37:08
Dernière modification le : mercredi 29 novembre 2017 - 15:53:16

### Citation

Paul Bourgade, Ashkan Nikeghbali, Alain Rouault. Ewens measures on compact groups and hypergeometric kernels. Séminaire de Probabilités XLIII, 2009, France. 2006, pp.351-377, 2011, 〈10.1007/978-3-642-15217-7〉. 〈hal-00690322〉

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