105 citations · 490 across the 24 of their papers we have counts for
26 papers
Asymptotics of Learning with Deep Structured (Random) Features
Dominik Schröder, Daniil Dmitriev, Hugo Cui +1
For a large class of feature maps we provide a tight asymptotic characterisation of the test error associated with learning the readout layer, in the high-dimensional limit where t…
Mesoscopic Central Limit Theorem for non-Hermitian Random Matrices
Giorgio Cipolloni, László Endős, Dominik Schröder
We prove that the mesoscopic linear statistics of the eigenvalues of large non-Hermitian random matrices with complex centred i.i.d…
Directional Extremal Statistics for Ginibre Eigenvalues
Giorgio Cipolloni, László Erdős, Dominik Schröder +1
We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum…
On the rightmost eigenvalue of non-Hermitian random matrices
Giorgio Cipolloni, László Erdős, Dominik Schröder +1
We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an random matrix with independent id…
Rank-uniform local law for Wigner matrices
Giorgio Cipolloni, László Erdős, Dominik Schröder
We prove a general local law for Wigner matrices which optimally handles observables of arbitrary rank and thus it unifies the well-known averaged and isotropic local laws. As an a…
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…
Functional Central Limit Theorems for Wigner Matrices
Giorgio Cipolloni, László Erdős, Dominik Schröder
We consider the fluctuations of regular functions of a Wigner matrix viewed as an entire matrix . Going beyond the well studied tracial mode, , whi…
Eigenstate Thermalization Hypothesis for Wigner Matrices
Giorgio Cipolloni, László Erdős, Dominik Schröder
We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversel…
Fluctuation Around the Circular Law for Random Matrices with Real Entries
Giorgio Cipolloni, László Erdős, Dominik Schröder
We extend our recent result [Cipolloni, Erdős, Schröder 2019] on the central limit theorem for the linear eigenvalue statistics of non-Hermitian matrices with independent, iden…
Central Limit Theorem for Linear Eigenvalue Statistics of non-Hermitian Random Matrices
Giorgio Cipolloni, László Erdős, Dominik Schröder
We consider large non-Hermitian random matrices with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are…
Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble
Giorgio Cipolloni, László Erdős, Dominik Schröder
We consider the least singular value of a large random matrix with real or complex i.i.d. Gaussian entries shifted by a constant . We prove an optimal lower tail es…
Edge Universality for non-Hermitian Random Matrices
Giorgio Cipolloni, László Erdős, Dominik Schröder
We consider large non-Hermitian real or complex random matrices with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near…
Cusp Universality for Random Matrices II: The Real Symmetric Case
Giorgio Cipolloni, László Erdős, Torben Krüger +1
We prove that the local eigenvalue statistics of real symmetric Wigner-type matrices near the cusp points of the eigenvalue density are universal. Together with the companion paper…
Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case
László Erdős, Torben Krüger, Dominik Schröder
For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp sing…
Correlated Random Matrices: Band Rigidity and Edge Universality
Johannes Alt, László Erdős, Torben Krüger +1
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 ed…
Random Matrices with Slow Correlation Decay
László Erdős, Torben Krüger, Dominik Schröder
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for…
Fluctuations of Functions of Wigner Matrices
László Erdős, Dominik Schröder
We show that matrix elements of functions of Wigner matrices fluctuate on a scale of order and we identify the limiting fluctuation. Our result holds for any…