Gaussuan limit for projective characters of large symmetric groups

In the 1993 S. Kerov obtained a central limit theorem for the Plansherel measure on Young diagrams. The Plansherel measure is a natural probability measure on the set of irredcible characters of the symmetric group $S_n$. Kerov's theorem states that, as $n\to\infty$, the values of irreducible characters on the simple cycles, appropriately normalized and considered as random variables, are asymptotically independent and converge to Gaussian random variables. In this work we obtain an analogue of this theorem for projective representations of the symmetric group.