A limit theorem on the shape of Ferrers graphs

We study the asymptotic behaviour of the $s$th largest part $L_{s,n}$ in a random partition of a positive integer $n$ as $n\to\infty$. The weak convergence of the distribution of $L_{s,n}$ to the Gaussian distribution is established provided $s$ is of order $n^{1/2}$ and $n\to\infty$.
The work was supported by the Bulgarian Ministry of Education, Science, and Technologies, contract 705/97. A part of the work was done during author's visit at the Steklov Mathematical Institute of the Russian Academy of Sciences.