On limit distributions of order statistics of a multinomial distribution

Let the equiprobable multinomial distribution (with all cell probabilities equal) have $N$ categories and sample size $n$. By $\varkappa_1(n,N),\dots,\varkappa_N(n,N)$ we denote the sampling frequencies arranged in the increasing order. This paper deals with the study of asymptotic behaviour ofj order statistics $\varkappa_k(n,N)$, $k=1,\dots,N$ as $n,N\to\infty$ so that $n/N\ln N\le C<\infty$.