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Abstract : |
We show in this paper that the Plancherel measure of the symmetric group Sn converges weakly (as n!1) to a Gaussian random process in the infinite dimensional vector space. With respect to the law of large numbers for this group, found earlier in [1,2] this assertion is analogous to the central limit theorem. The idea of such a result was mentioned in [3]. In the course of preparation of the article I had numerous valuable conversations with A.Vershik and G.Olshanski. In particular, it was Olshanski who suggested to use Lemma 2.3 below while discussing the preliminary version of the paper. 1. Main results. Let Sn be the symmetric group of degree n and b Sn-- the set (of equivalence classes) of its irreducible representations. The character of a representation 2 b Sn will be denoted as, |
