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Asymptotics of multinomial sums and identities between multi-integrals

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Abstract

We calculate the asymptotics of combinatorial sums ∑ α f(α)( n α )β, whereα = (α 1, …,α h ) withα i =α j for certaini, j. Hereh is fixed and theα i ’s are natural numbers. This implies the asymptotics of the correspondingS n -character degrees ∑λ f(λ)d βλ . For certain sequences ofS n characters which involve Young’s rule, the latter asymptotics were obtained earlier [1] by a different method. Equating the two asymptotics, we obtain equations between multi-integrals which involve Gaussian measures. Special cases here give certain extensions of the Mehta integral [5], [6].

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Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, 08540, Princeton, NJ, USA

    Paula Beazley Cohen

  2. URA Géométrie-Analyse-Topologie, Université des Sciences et Technologies de Lille, 59655, Villeneuve d’Ascq cedex, France

    Paula Beazley Cohen

  3. Department of Mathematics, The Pennsylvania State University, 16802, University Park, PA, USA

    Amitai Regev

  4. Department of Theoretical Mathematics, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Amitai Regev

Authors
  1. Paula Beazley Cohen
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  2. Amitai Regev
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Corresponding author

Correspondence to Paula Beazley Cohen.

Additional information

Supported by the Weizmann Institute of Science, Rehovot, Israel; by the Institute for Advanced Study, Princeton, New Jersey, USA; NSF grant number DMS 9304580; and by the Centre National de Recherche Scientifique, Lille, France.

This work was partially supported by an NSF grant number DMS 94-01197.

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Cohen, P.B., Regev, A. Asymptotics of multinomial sums and identities between multi-integrals. Isr. J. Math. 112, 301–325 (1999). https://doi.org/10.1007/BF02773486

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  • DOI: https://doi.org/10.1007/BF02773486

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