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A statistical sum associated with Young diagrams

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Abstract

We study the asymptotics of sums of powers of normalized dimensions of complex irreducible representations of the symmetric group

as N→∞. We calculate the limit Gibbs measure on the space of Young diagrams. The problem is connected with a one-dimensional model of statistical physics. In the appendix, written by A. M. Pass, numerical and graphical data about the free energy corresponding to the statistical studied are given.

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Literature cited

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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 164, pp. 20–29, 1987.

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Vershik, A.M. A statistical sum associated with Young diagrams. J Math Sci 47, 2379–2386 (1989). https://doi.org/10.1007/BF01840420

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  • DOI: https://doi.org/10.1007/BF01840420

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