Some results on random circulant matrices

Abstract

This paper considers random (non-Hermitian) circulant matrices, and proves several results analogous to recent theorems on non-Hermitian random matrices with independent entries. In particular, the limiting spectral distribution of a random circulant matrix is shown to be complex normal, and bounds are given for the probability that a circulant sign matrix is singular.

References in corpus (7)

• Universality at the edge of the spectrum in Wigner random matrices
• Spectral measure of large random Hankel, Markov and Toeplitz matrices
• Eigenvalue Spacing Distribution for the Ensemble of Real Symmetric Toeplitz Matrices
• A characterization of dimension free concentration in terms of transportation inequalities
• Concentration of norms and eigenvalues of random matrices
• A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices
• Bounds on the concentration function in terms of Diophantine approximation

Cited by in corpus (8)

• Around the circular law
• The asymptotic distribution of the condition number for random circulant matrices
• The spectra of random abelian G-circulant matrices
• Salem-Zygmund Inequality for locally sub-Gaussian random variables, random trigonometric polynomials, and random circulant matrices
• Extremal Laws for Laplacian Random Matrices
• On $\ast$-Convergence of Schur-Hadamard Products of Independent Nonsymmetric Random Matrices
• Quenched Central Limit Theorem in a Corner Growth Setting
• Concentration of the empirical spectral distribution of random matrices with dependent entries