12 papers · 1 filter
Local law and delocalization for the Sachdev-Ye-Kitaev model
Lucas Benigni, Giorgio Cipolloni
We establish a mesoscopic local law and quantitative eigenvector-delocalization estimates for the Sachdev--Ye--Kitaev model (SYK) Hamiltonian of interacting Majorana fermions.…
The eigenvalues of i.i.d. matrices are hyperuniform
Giorgio Cipolloni, László Erdős, Oleksii Kolupaiev
We prove that the point process of the eigenvalues of real or complex non-Hermitian matrices with independent, identically distributed entries is hyperuniform: the variance of…
Numerical Radius of Non-Hermitian Random Matrices
Zhigang Bao, Giorgio Cipolloni
For a square matrix, the range of its Rayleigh quotients is known as the numerical range, which is a compact and convex set by the Toeplitz-Hausdorff theorem. The largest value and…
Optimal Delocalization for Non--Hermitian Eigenvectors
Giorgio Cipolloni, Benjamin Landon
We prove an optimal order delocalization estimate for the eigenvectors of general non-Hermitian matrices : wi…
Law of fractional logarithm for random matrices
Zhigang Bao, Giorgio Cipolloni, László Erdős +2
We prove the Paquette-Zeitouni law of fractional logarithm (LFL) for the extreme eigenvalues [arXiv:1505.05627] in full generality, and thereby verify a conjecture from [arXiv:1505…
Decorrelation transition in the Wigner minor process
Zhigang Bao, Giorgio Cipolloni, László Erdős +2
We consider the Wigner minor process, i.e. the eigenvalues of an Wigner matrix together with the eigenvalues of all its minors, , $n\le N…