Stein’s method and Plancherel measure of the symmetric group

DOI10.1090/S0002-9947-04-03499-3zbMath1054.05099arXivmath/0305423OpenAlexW1849645519MaRDI QIDQ4825665

Jason Fulman

Publication date: 28 October 2004

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0305423

zbMATH Keywords

Plancherel measureStein's methodMarkov chainirreducible representations of the symmetric groupcharacter ratio

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Combinatorial probability (60C05)

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Markov processes on partitions, Stein's method for concentration inequalities, Two-parameter family of infinite-dimensional diffusions on the Kingman simplex, \(\mathfrak{sl}(2)\) operators and Markov processes on branching graphs, A down‐up chain with persistent labels on multifurcating trees, Stein's method and random character ratios, Random walks on strict partitions, Separation cutoffs for random walk on irreducible representations, Step Size in Stein's Method of Exchangeable Pairs, The Saxl conjecture for fourth powers via the semigroup property, Convergence rates of random walk on irreducible representations of finite groups, The law of the iterated logarithm for character ratios, Stein's method, Jack measure, and the Metropolis algorithm, Commutation relations and Markov chains, Infinite-dimensional diffusions as limits of random walks on partitions, Spectra of random linear combinations of matrices defined via representations and Coxeter generators of the symmetric group, Martingales and character ratios, Zero Biasing and Jack Measures, Noncolliding Jacobi processes as limits of Markov chains on the Gelfand-Tsetlin graph, Effect of microscopic pausing time distributions on the dynamical limit shapes for random Young diagrams, New error bounds in multivariate normal approximations via exchangeable pairs with applications to Wishart matrices and fourth moment theorems

Cites Work

• Stein's method, Jack measure, and the Metropolis algorithm
• Representations of symmetric groups and free probability
• Central limit theorem for the adjacency operators on the infinite symmetric group
• Comparison techniques for random walk on finite groups
• On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted \(U\)-statistics
• Poisson approximation and the Chen-Stein method. With comments and a rejoinder by the authors
• Card shuffling and the decomposition of tensor products.
• Harmonic functions on multiplicative graphs and interpolation polynomials
• Generating a random permutation with random transpositions
• Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem
• Analysis of Top To Random Shuffles
• Asymptotics of Plancherel measures for symmetric groups
• Discrete orthogonal polynomial ensembles and the Plancherel measure
• Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials
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