Counting formulas associated with some random matrix averages

  • Authors:

  • Peter J. Forrester;Alex Gamburd

  • Affiliations:

  • Department of Mathematics and Statistics, University of Melbourne, Victoria, Australia;Department of Mathematics, University of California, Santa Cruz, CA and Department of Mathematics, Stanford University, Stanford, CA

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2006

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Abstract

Moments of secular and inverse secular coefficients, averaged over random matrices from classical groups, are related to the enumeration of non-negative matrices with prescribed row and column sums. Similar random matrix averages are related to certain configurations of vicious random walkers and to the enumeration of plane partitions. The combinatorial meaning of the average of the characteristic polynomial of random Hermitian and Wishart matrices is also investigated, and consequently several simple universality results are derived.