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Article

Центральная предельная теорема для экстремальных характеров бесконечной симметрической группы

Буфетов А. И.

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.