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Hoeffding spaces and Specht modules

Published online by Cambridge University Press:  15 October 2010

Giovanni Peccati  and
Jean-Renaud Pycke
Giovanni Peccati
Affiliation:
Équipe , Université Paris Ouest-Nanterre La Dé fense, 200 avenue de la République, 92000 Nanterre, France. giovanni.peccati@gmail.com
Jean-Renaud Pycke
Affiliation:
Département de Mathématiques, Université d'Évry, Évry, France; jrpycke@maths.univ-evry.fr
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Abstract

It is proved that each Hoeffding space associated with a random permutation(or, equivalently, with extractions without replacement from a finitepopulation) carries an irreducible representation of the symmetric group,equivalent to a two-block Specht module.

Keywords

Exchangeabilityfinite populationstatisticsHoeffding decompositionsirreducible representationsrandompermutationsSpecht modulessymmetric group
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 15: Supplement: In honor of Marc Yor , 2011 , pp. S58 - S68
Copyright
© EDP Sciences, SMAI, 2011

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