Israel Journal of Mathematics

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

Asymptotics of multinomial sums and identities between multi-integrals

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Abstract

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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References

  1. [1]
    W. Beckner and A. Regev,Asymptotic estimates using Probability, Advances in Mathematics138 (1998), 1–14.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    W. Beckner and A. Regev,Coefficients in some Young derived sequences, European Journal of Combinatorics17 (1996), 689–697.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    P. Cohen and A. Regev,Asymptotics of combinatorial sums and the central limit theorem, SIAM Journal on Mathematical Analysis19 (1988), 1204–1215.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    I. G. MacDonald,Symmetric Functions and Hall Polynomials, 2nd edn., Oxford University (Clarendon) Press, 1995.Google Scholar
  5. [5]
    I. G. MacDonald,Some conjectures for root systems and finite reflection groups, SIAM Journal on Mathematical Analysis41 (1981), 998–1007.Google Scholar
  6. [6]
    M. L. Mehta,Random Matrices, Academic Press, New York, 1967.MATHGoogle Scholar
  7. [7]
    A. Regev,Asymptotics values for degrees associated with strips of Young diagrams, Advances in Mathematics42 (1981), 115–136.CrossRefMathSciNetGoogle Scholar
  8. [8]
    A. Regev,Young-derived sequences of S n-characters, Advances in Mathematics106 (1994), 169–197.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    A. Selberg,Bemerkninger om et multipelt integral, Nordisk Matematisk Tidskrift26 (1944), 71–78.MATHMathSciNetGoogle Scholar

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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