Hard and soft edge spacing distributions for random matrix ensembles with orthogonal and symplectic symmetry

2006/05/06 by Peter J. Forrester, Forrester, P. J. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.math-ph/0605022

openalex publication_date 2006/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inter-relations between random matrix ensembles with different symmetry types provide inter-relations between generating functions for the gap probabilites at the spectrum edge. Combining these in the scaled limit with the exact evaluation of the gap probabilities for certain superimposed ensembles with orthogonal symmetry allows for the exact evaluation of the gap probabilities at the hard and soft spectrum edges in the cases of orthogonal and symplectic symmetry. These exact evaluations are given in terms of Painlevé transcendents, and in terms of Fredholm determinants.

Cited by

• Asymptotic Expansions of Gaussian and Laguerre Ensembles at the Soft Edge III: Generating Functions

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