Central limit theorem for random strict partition

We consider a set of partitions of number $n$ on distinct summands (so called strict partitions) with uniform distribution on it. We investigate fluctuations of random partition near its limit shape, for large $n$. Usage of geometrical language allows to state the problem in terms of limit behaviour of random step functions (Young diagram). Central limit theorem for such functions is proven.
The method of investigation essentially uses the notion of large canonical ensemble of partitions.