  The asymptotics of the first rows and columns of random Young diagrams
corresponding to extremal characters of the infinite symmetric group is
studied. We consider rows and columns with linear growth in $n$, the number of
boxes of random diagrams, and prove the central limit theorem for them in the
case of distinct Thoma parameters. We also establish a more precise statement
relating the growth of rows and columns of Young diagrams to a simple
independent random sampling model.
  After this paper was completed, the author learned that the central limit
theorem has been also proved in the work of M\'eliot (arXiv:1105.0091v1) by a
different method.
