Israel Journal of Mathematics

, Volume 112, Issue 1, pp 301–325

Asymptotics of multinomial sums and identities between multi-integrals


    • School of MathematicsInstitute for Advanced Study
    • URA Géométrie-Analyse-TopologieUniversité des Sciences et Technologies de Lille
  • Amitai Regev
    • Department of MathematicsThe Pennsylvania State University
    • Department of Theoretical MathematicsThe Weizmann Institute of Science

DOI: 10.1007/BF02773486

Cite this article as:
Cohen, P.B. & Regev, A. Isr. J. Math. (1999) 112: 301. doi:10.1007/BF02773486


We calculate the asymptotics of combinatorial sums ∑αf(α)(αn)β, whereα = (α1, …,αh) withαi =αj for certaini, j. Hereh is fixed and theαi’s are natural numbers. This implies the asymptotics of the correspondingSn-character degrees ∑λf(λ)dλβ. For certain sequences ofSn 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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© Hebrew University 1999