Correlated Random Matrices: Band Rigidity and Edge Universality

Abstract

We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models.

26 pages. In the new version we included a self-contained analysis of general square-root edges of the density of states

References in corpus (5)

• Random Matrices with Slow Correlation Decay
• On the edge universality of the local eigenvalue statistics of matrix models
• Cusp Universality for Random Matrices II: The Real Symmetric Case
• Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case
• Transition from Tracy-Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erdős-Rényi graphs

Cited by in corpus (9)

• Spectral radius of random matrices with independent entries
• Convergence rate to the Tracy-Widom laws for the largest eigenvalue of Wigner matrices
• Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case
• Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrices and sample covariance matrices
• Infinite stable Boltzmann planar maps are subdiffusive
• Dynamics of a rank-one perturbation of a Hermitian matrix
• Large deviations for the largest eigenvalue of matrices with variance profiles
• On fluctuations of global and mesoscopic linear eigenvalue statistics of generalized Wigner matrices
• On the operator norm of a Hermitian random matrix with correlated entries