Israel Journal of Mathematics

, Volume 112, Issue 1, pp 301–325

Asymptotics of multinomial sums and identities between multi-integrals

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Abstract

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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Copyright information

© 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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