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

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.

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.

DOI: 10.1214/12-AIHP519
Classification: 05D40,  05E10,  20C30,  60C05
Keywords: 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, Volume 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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