Hoeffding spaces and Specht modules

Giovanni Peccati (1, 2) , Jean-Renaud Pycke (3)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 MODAL'X - Modélisation aléatoire de Paris X
3 Département de Mathématiques (Evry)

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

Mots clés: Exchangeability; Finite Population Statistics; Hoeffding Decompositions; Irreducible Representations; Random Permutations; Specht Modules; Symmetric Group

Domaines: Probabilités [math.PR]; Théorie des groupes [math.GR]

Giovanni Peccati, Jean-Renaud Pycke. Hoeffding spaces and Specht modules. 2009. ⟨hal-00377086⟩