A central limit theorem for the characters of the infinite symmetric group and of the infinite Hecke algebra

Details A central limit theorem for the characters of the infinite symmetric group and of the infinite Hecke algebra A central limit theorem for the characters of the infinite symmetric group and of the infinite Hecke algebra

2011-04-30

arxiv.org/abs/1105.0091v1

Mathematics

Representation Theory

70 pages, 9 figures

Scientific paper

In this paper, we review the representation theory of the infinite symmetric group, and we extend the works of Kerov and Vershik by proving that the irreducible characters of the infinite symmetric group always satisfy a central limit theorem. Hence, for any point of the Thoma simplex, the corresponding measures on the levels of the Young graph have a property of gaussian concentration. By using the Robinson-Schensted-Knuth algorithm and the theory of Pitman operators, we relate these results to the properties of certain random permutations obtained by riffle shuffles, and to the behaviour of random walks conditioned to stay in a Weyl chamber.

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