Gaussian Limit for Projective Characters of Large Symmetric Groups

Abstract

In 1993, S. Kerov obtained a central limit theorem for the Plancherel measure on Young diagrams. The Plancherel measure is a natural probability measure on the set of irreducible characters of the symmetric group S n. Kerov's theorem states that, as n→∞, the values of irreducible characters at simple cycles, appropriately normalized and considered as random variables, are asymptotically independent and converge to Gaussian random variables. In the present work we obtain an analog of this theorem for projective representations of the symmetric group. Bibliography: 27 titles.