Asymptotics of \(q\)-Plancherel measures.

DOI10.1007/s00440-010-0331-6zbMath1250.20075arXiv1001.2180OpenAlexW1988960617MaRDI QIDQ2428504

Valentin Féray, Pierre-Loïc Méliot

Publication date: 26 April 2012

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.2180

zbMATH Keywords

Hecke algebrasPlancherel measureYoung diagramsrandom partitionspartitions of integerslimiting shape

Mathematics Subject Classification ID

Related Items (10)

Macdonald cumulants, \(G\)-inversion polynomials and \(G\)-parking functions ⋮ A combinatorial formula for Macdonald cumulants ⋮ A central limit theorem for extremal characters of the infinite symmetric group. ⋮ Partial isomorphisms over finite fields ⋮ Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category ⋮ Core size of a random partition for the Plancherel measure ⋮ Strong factorization property of Macdonald polynomials and higher-order Macdonald's positivity conjecture ⋮ Statistical properties of eigenvalues of Laplace-Beltrami operators ⋮ Law of large numbers for infinite random matrices over a finite field ⋮ Lengths of monotone subsequences in a Mallows permutation

Uses Software

• SageMath
• Sage-Combinat

Cites Work

• Applications of the Frobenius formulas for the characters of the symmetric group and the Hecke algebras of type A
• Harmonic analysis on the infinite symmetric group
• Induced cuspidal representations and generalised Hecke rings
• A Frobenius formula for the characters of the Hecke algebras
• A variational problem for random Young tableaux
• A note on Harish-Chandra induction
• A \(q\)-analog of the hook walk algorithm and random Young tableaux
• On the distribution of the length of the second row of a Young diagram under Plancherel measure
• Asymptotic theory of characters of the symmetric group
• The law of large numbers and the central limit theorem for the Jordan normal form of large triangular matrices over a finite field
• A differential model for the deformation of the Plancherel growth process
• Gaussian fluctuations of characters of symmetric groups and of Young diagrams
• The calculation of cumulants via conditioning
• Die unzerlegbaren, positiv-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe
• Combinatorics of the \(q\)-basis of symmetric functions
• Characters of Reductive Groups over a Finite Field. (AM-107)
• On a Method of Calculation of Semi-Invariants
• Representations of Lie groups and random matrices
• On the distribution of the length of the longest increasing subsequence of random permutations
• Asymptotics of Plancherel measures for symmetric groups
• Discrete orthogonal polynomial ensembles and the Plancherel measure
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