Matrix Kernels for the Gaussian Orthogonal and Symplectic Ensembles

Abstract

We derive the limiting matrix kernels for the the Gaussian Orthogonal and Symplectic ensembles scaled at the edge, with proofs of convergence in the operator norms that assure convergence of the determinants.

10 pages, LaTeX

References in corpus (5)

• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges
• Distribution functions for largest eigenvalues and their applications
• Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
• Toeplitz determinants, random growth and determinantal processes

Cited by in corpus (2)

• Universality at the edge of the spectrum for unitary, orthogonal and symplectic ensembles of random matrices
• Distribution Functions for Edge Eigenvalues in Orthogonal and Symplectic Ensembles: Painlevé Representations II