105 citations · 490 across the 24 of their papers we have counts for
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Optimal multi-resolvent local laws for Wigner matrices
Giorgio Cipolloni, László Erdős, Dominik Schröder
We prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the si…
On the Spectral Form Factor for Random Matrices
Giorgio Cipolloni, László Erdős, Dominik Schröder
In the physics literature the spectral form factor (SFF), the squared Fourier transform of the empirical eigenvalue density, is the most common tool to test universality for disord…
Density of small singular values of the shifted real Ginibre ensemble
Giorgio Cipolloni, László Erdős, Dominik Schröder
We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter as the dimension tends to…
Quenched universality for deformed Wigner matrices
Giorgio Cipolloni, László Erdős, Dominik Schröder
Following E. Wigner's original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix yields the celebrated Wigner-Dyso…
On the condition number of the shifted real Ginibre ensemble
Giorgio Cipolloni, László Erdős, Dominik Schröder
We derive an accurate lower tail estimate on the lowest singular value of a real Gaussian (Ginibre) random matrix shifted by a complex parameter . Such shift effe…
Analysis of One-Hidden-Layer Neural Networks via the Resolvent Method
Vanessa Piccolo, Dominik Schröder
In this work, we investigate the asymptotic spectral density of the random feature matrix with generated by a single-hidden-layer neural network, where $…
Normal fluctuation in quantum ergodicity for Wigner matrices
Giorgio Cipolloni, László Erdős, Dominik Schröder
We consider the quadratic form of a general deterministic matrix on the eigenvectors of an Wigner matrix and prove that it has Gaussian fluctuation for each bulk eigenv…
Thermalisation for Wigner matrices
Giorgio Cipolloni, László Erdős, Dominik Schröder
We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices and provide an optimal error bound on their fluctuation with very high prob…