Entropy of Schur-Weyl measures
Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 2, pp. 678-713.

Les dimensions relatives des composants isotypiques des représentations tensorielles du Nième ordre du groupe symétrique sur n lettres induisent une mesure du type Plancherel sur l’espace des diagrammes de Young avec n cellules et au plus N rangs. G. Olshanski a conjecturé que ces dimensions, après renormalisation, convergent vers une constante sous cette famille de mesures du type Plancherel dans la limite où N n converge vers une constante. Le principal résultat de cet article est la preuve de cette conjecture.

Relative dimensions of isotypic components of Nth 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 result of the paper is the proof of this conjecture.

DOI : 10.1214/12-AIHP519
Classification : 05D40, 05E10, 20C30, 60C05
Mots clés : asymptotic representation theory, Schur-Weyl duality, Plancherel measure, Schur-Weyl measure, Vershik-Kerov conjecture
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Mkrtchyan, Sevak. Entropy of Schur-Weyl measures. Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 2, pp. 678-713. doi : 10.1214/12-AIHP519. http://www.numdam.org/articles/10.1214/12-AIHP519/

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