Israel Journal of Mathematics

, Volume 112, Issue 1, pp 301–325 | Cite as

Asymptotics of multinomial sums and identities between multi-integrals



We calculate the asymptotics of combinatorial sums ∑ α f(α)( α n ) 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 λ β . 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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© Hebrew University 1999

Authors and Affiliations

  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonUSA
  2. 2.URA Géométrie-Analyse-TopologieUniversité des Sciences et Technologies de LilleVilleneuve d’Ascq cedexFrance
  3. 3.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA
  4. 4.Department of Theoretical MathematicsThe Weizmann Institute of ScienceRehovotIsrael

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