  We study asymptotics of reducible representations of the symmetric groups S_q
for large q. We decompose such a representation as a sum of irreducible
components (or, alternatively, Young diagrams) and we ask what is the character
of a randomly chosen component (or, what is the shape of a randomly chosen
Young diagram). Our main result is that for a large class of representations
the fluctuations of characters (and fluctuations of the shape of the Young
diagrams) are asymptotically Gaussian; in this way we generalize Kerov's
central limit theorem. The considered class consists of representations for
which the characters almost factorize and this class includes, for example,
left-regular representation (Plancherel measure), tensor representations. This
class is also closed under induction, restriction, outer product and tensor
product of representations. Our main tool in the proof is the method of genus
expansion, well known from the random matrix theory.
