Averages over Ginibre's Ensemble of Random Real Matrices

2006/05/02 by Christopher D. Sinclair, Sinclair, Christopher D. · 1 citation
Mathematics · Physics and Astronomy · #15A52 #15A90 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications #math-ph #math.MP #msc:15A52 #msc:15A90

paper · pdf · doi:10.48550/arxiv.math-ph/0605006

12 pages

arxiv created 2006/05/02 · openalex publication_date 2006/05/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a method for computing the ensemble average of multiplicative class functions over the Gaussian ensemble of real asymmetric matrices. These averages are expressed in terms of the Pfaffian of Gram-like antisymmetric matrices formed with respect to a skew-symmetric inner product related to the class function.

Cited by

• Moderate-to-large deviation asymptotics for real eigenvalues of the elliptic Ginibre matrices

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• Correlation Functions of Asymmetric Real Matrices
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