Ensemble averages when β is a square integer

Abstract

We give a hyperpfaffian formulation of partition functions and ensemble averages for Hermitian and circular ensembles when L is an arbitrary integer and β = L 2 and when L is an odd integer and β = L 2 + 1.

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Correspondence to Christopher D. Sinclair.

Additional information

This research was supported in part by the National Science Foundation (DMS-0801243).

Communicated by C. Krattenthaler.

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Sinclair, C.D. Ensemble averages when β is a square integer. Monatsh Math 166, 121–144 (2012). https://doi.org/10.1007/s00605-011-0371-8

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Keywords

  • Random matrix theory
  • Partition function
  • Pfaffian
  • Hyperpfaffian
  • Selberg integral

Mathematics Subject Classification (2010)

  • 15B52
  • 82C22
  • 60G55