Approximate factorization and concentration for characters of symmetric groups
By Philippe Biane. 2000
101 citations recorded by the source corpus.
We prove a factorization-concentration result for characters of symmetric groups. This is then applied to the asymptotic behaviour of the decomposition of the tensor representations. There are connections with the Pastur-Marcenko distribution of random matrix theory, and freely infinitely divisible distributions.
Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/ff3b8bf959ef9ca248dadfde678d2e3935992a69
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In Discrete Mathematics and Combinatorics
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Asymptotics of characters of symmetric groups related to Stanley character formula (2007, methodology): “of information about the representation ρλis contained in the distribution of the random Young diagram λ˜. The importance of the approximate factorization of characters (8) was pointed out in a paper [Bia01] where Biane proved that it implies some analogue of the law of large numbers for √1 n ˜λ n; ”
- Efficient quantum tomography (2015, unknown): “ered the case of uniform α in the nonasymptotic setting. Here, rather than fixing d and letting n tend towards infinity, d is allowed to grow to infinity while n scales as n = O(d2). In this case, Biane [Bia01] has shown a limiting theorem for the shape of λ, and M´eliot [M´el10] has characterized the ”
- Gaussian fluctuations of characters of symmetric groups and of Young diagrams (2005, methodology): “ pl1+l2−2r for all integers l,l1,l2 ≥ 1. Note that for p =0 we recover the fluctuations of the Plancherel measure. 14 PIOTR SNIADY´ Some asymptotic results for this representation were proved by Biane [Bia01]. Example 3.6 (Irreducible representations). Let c > 0 be a constant and let (λq)be a sequ”