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Entropy of Schur–Weyl measures

Sevak Mkrtchyan (2014)

Annales de l'I.H.P. Probabilités et statistiques

Relative dimensions of isotypic components of N th order tensor representations of the symmetric group on n letters give a Plancherel-type measure on the space of Young diagrams with n cells and at most N rows. It was conjectured by G. Olshanski that dimensions of isotypic components of tensor representations of finite symmetric groups, after appropriate normalization, converge to a constant with respect to this family of Plancherel-type measures in the limit when N n converges to a constant. The main...

Exact distribution under independence of the diagonal section of the empirical copula

Arturo Erdely, José M. González–Barrios (2008)

Kybernetika

In this paper we analyze some properties of the empirical diagonal and we obtain its exact distribution under independence for the two and three- dimensional cases, but the ideas proposed in this paper can be carried out to higher dimensions. The results obtained are useful in designing a nonparametric test for independence, and therefore giving solution to an open problem proposed by Alsina, Frank and Schweizer [2].

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