Application of Random Matrix Theory to Multivariate Statistics

Abstract

This is an expository account of the edge eigenvalue distributions in random matrix theory and their application in multivariate statistics. The emphasis is on the Painlevé representations of these distributions.

References in corpus (2)

• Universality at the edge of the spectrum for unitary, orthogonal and symplectic ensembles of random matrices
• Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues

Cited by in corpus (11)

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• The Spectrum of the Axion Dark Sector
• Rarefaction Waves of the Korteweg-de Vries Equation via Nonlinear Steepest Descent
• Typical versus averaged overlap distribution in Spin-Glasses : Evidence for the droplet scaling theory
• A random matrix approach to the boson peak and Ioffe-Regel criterion in amorphous solids
• Mixed moments of characteristic polynomials of random unitary matrices
• Linear Statistics of Random Matrix Ensembles at the Spectrum Edge Associated with the Airy Kernel
• On the probability of positive-definiteness in the gGUE via semi-classical Laguerre polynomials
• BKP hierarchy and Pfaffian point process
• Hamiltonian structure of rational isomonodromic deformation systems
• Central Limit Theorem for Linear Eigenvalue Statistics for Submatrices of Wigner Random Matrices