Giorgio Cipolloni

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 $N$ interacting Majorana fermions s…

math-ph2026

On a Rosenzweig-Porter-type model

Giorgio Cipolloni, László Erdős, Joscha Henheik

We consider a very general Rosenzweig-Porter-type model, $H = H_{0} + λW$ , where $H_{0}$ is an arbitrary Hermitian matrix and $W$ is a standard Wigner matrix. We precisely trace the locali…

Sobolev convergence of log-determinants for smooth Wigner matrices

Giorgio Cipolloni, Patrick Lopatto

We show that the fields emerging from the log-determinant and the eigenvalue counting function of smooth Wigner matrices converge in law to centered Gaussian, logarithmically corre…

The non-Hermitian minor process

Giorgio Cipolloni, László Erdős, Oleksii Kolupaiev

We show that the log-determinant of leading principal minors of large non-Hermitian random matrices converges in distribution to a 2+1 dimensional Gaussian field, which is logarith…

Gaussian Multiplicative Chaos for i.i.d. matrices

Giorgio Cipolloni, Benjamin Landon

We consider $N \times N$ matrices $X$ with i.i.d. entries, and prove that the random measure $μ_N(z):=\frac{ | \det (X-z)|^γ}{\mathbb{E}[ | \det (X-z)|^γ]} \mathrm{d} z\mathrm{d} \o…

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 $X$ 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 $N \times N$ non-Hermitian matrices $X$ : $∥ v ∥_{\infty} \leq C \frac{l o g N}{N}$ 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 $N \times N$ Wigner matrix $H^{(N)}$ together with the eigenvalues of all its $n \times n$ minors, $H^{(n)}$ , $n\le N…

Optimal decay of eigenvector overlap for non-Hermitian random matrices

Giorgio Cipolloni, László Erdős, Yuanyuan Xu

We consider the standard overlap $O_{ij} := ⟨ r_{j}, r_{i} ⟩ ⟨ l_{j}, l_{i} ⟩$ of any bi-orthogonal family of left and rig…

Eigenvector decorrelation for random matrices

Giorgio Cipolloni, László Erdős, Joscha Henheik +1

We study the sensitivity of the eigenvectors of random matrices, showing that even small perturbations make the eigenvectors almost orthogonal. More precisely, we consider two defo…

math.PR2024★ 1 cited

Non-Hermitian spectral universality at critical points

Giorgio Cipolloni, László Erdős, Hong Chang Ji

For general large non-Hermitian random matrices $X$ and deterministic normal deformations $A$ , we prove that the local eigenvalue statistics of $A + X$ close to the critical edge poi…

Fluctuations for non-Hermitian dynamics

Paul Bourgade, Giorgio Cipolloni, Jiaoyang Huang

We prove that under the Brownian evolution on large non-Hermitian matrices the log-determinant converges in distribution to a 2+1 dimensional Gaussian field in the Edwards-Wilkinso…

Matrix Concentration Inequalities and Free Probability II. Two-sided Bounds and Applications

Afonso S. Bandeira, Giorgio Cipolloni, Dominik Schröder +1

The first paper in this series introduced a new family of nonasymptotic matrix concentration inequalities that sharply capture the spectral properties of very general random matric…

Maximum of the Characteristic Polynomial of I.I.D. Matrices

Giorgio Cipolloni, Benjamin Landon

We compute the leading order asymptotic of the maximum of the characteristic polynomial for i.i.d. matrices with real or complex entries. In particular, this result is new even for…