Asymptotic Representation Theory of the Symmetric Group and its Applications in Analysis

By S. Kerov. 2003

244 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f986f66f7e04c3c02fc9d1627e6668d77d9b4609

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In Mathematical Physics

Citations in the corpus

Exchangeable Gibbs partitions and Stirling triangles (2004, result): “This result was conjectured in [12, 14], and also stated without proof in [17], attributed to Frank Kelly.”
Representations of the Infinite Symmetric Group (2016, background): “Coherent systems on the Young graph The notions discussed here originated in the works of Thoma [117] and Vershik and Kerov [121], [122], [124], [125], [126], [63].”
Inversion of the Pieri formula for Macdonald polynomials (2004, background): “This result had been given by Kerov [7, Th. 6.3] (see also [8]).”
Mod-ϕ Convergence (2016, background): “This definition of central measures comes from [KV81, Section 3], and it can be generalised to the setting of approximately finite algebras, see [SV75] and [Ker03].”
Representations of classical Lie groups and quantized free convolution (2013, methodology): “We need one particular way to associate a probability measure on R to a Young diagram λ, which is known as Kerov’s transition measure [K1], [K4].”
Combinatorial Stochastic Processes (2006, background): “In the work of Kerov and Vershik on multiplicative branchings [241, 242, 244], each extreme infinite exchangeable partition corresponds to a real-valued character of the algebra of symmetric functions, with certain positivity conditions.”
Macdonald processes (2011, background): “The classification is known in the case of nonnegative specializations of Jack’s symmetric functions [60] and in the subcase of Schur symmetric functions this is a classical statement known as “Thoma’s theorem” (see [59] and references therein).”
Harmonic analysis on the infinite symmetric group (2003, result): “= X νցλ f(ν) ∀λ ∈Y. The coherency relation for a function M(λ) is equivalent to the harmonicity relation for the function f(λ) = M(λ)/dimλ. For further details, see Vershik–Kerov [VK2], Kerov [Ker2], [Ker4]. 9.4. Central measures on paths and transition probabilities. By a path in the Young graph we”