Random matrices: The Four Moment Theorem for Wigner ensembles

Abstract

We survey some recent progress on rigorously establishing the universality of various spectral statistics of Wigner random matrix ensembles, focusing in particular on the Four Moment Theorem and its applications.

17 pages, no figures, submitted, MSRI book series

References in corpus (4)

• Local semicircle law and complete delocalization for Wigner random matrices
• Universality for mathematical and physical systems
• Bulk Universality for Wigner Matrices
• Average Density of States for Hermitian Wigner Matrices

Cited by in corpus (5)

• Local universality of repulsive particle systems and random matrices
• The Spectrum of Random Inner-product Kernel Matrices
• Density and spacings for the energy levels of quadratic Fermi operators
• Localization and delocalization of eigenvectors for heavy-tailed random matrices
• Bulk Universality for Generalized Wigner Matrices With Few Moments