Entropy of Schur-Weyl measures

DOI10.1214/12-AIHP519zbMath1290.05148arXiv1107.1541OpenAlexW2964285435MaRDI QIDQ2451116

Sevak Mkrtchyan

Publication date: 26 May 2014

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.1541

zbMATH Keywords

Plancherel measureSchur-Weyl dualityasymptotic representation theorySchur-Weyl measureVershik-Kerov conjecture

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Combinatorial probability (60C05) Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) (05D40)

Related Items (4)

Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so2n+1 ^* ⋮ A CLT for Plancherel representations of the infinite-dimensional unitary group ⋮ Entropy and the Shannon-McMillan-Breiman theorem for beta random matrix ensembles ⋮ Plancherel representations of \(U(\infty)\) and correlated Gaussian free fields

Cites Work

• The boundary of the Gelfand-Tsetlin graph: A new approach
• Asymptotics of the maximal and the typical dimensions of isotypic components of tensor representations of the symmetric group.
• On the Vershik-Kerov conjecture concerning the Shannon-McMillan-Breiman theorem for the Plancherel family of measures on the space of Young diagrams
• Asymptotics of Plancherel measures for the infinite-dimensional unitary group
• Difference operators and determinantal point processes
• Asymptotics of maximal and typical dimensions of irreducible representations of a symmetric group
• Représentations factorielles de type \(II_1\) de \(U(\infty)\)
• A variational problem for random Young tableaux
• Asymptotics of Plancherel-type random partitions
• Determinantal random point fields
• Asymptotics of Plancherel measures for symmetric groups
• Discrete orthogonal polynomial ensembles and the Plancherel measure
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