László Erdős

activity

20142026

most citedPhase Transition in the Density of States of Quantum Spin Glasses

105 citations · 119 across the 22 of their papers we have counts for

collaborators

23 papers

math.PR2026

Beyond normal fluctuations in local laws for Wigner matrices

László Erdős, Oleksii Kolupaiev

We identify non-Gaussian corrections to the central limit theorem for the global and local laws, i.e. for Stieltjes transform of the empirical eigenvalue distribution of a large re…

math-ph2026

Anomalous rate of eigenstate thermalisation at singularities of the density of states

László Erdős, Joscha Henheik, Volodymyr Riabov

We prove the Eigenstate Thermalisation Hypothesis (ETH), also known as Quantum Unique Ergodicity (QUE), for large $N \times N$ mean-field random matrices with general correlation st…

math-ph2025

Normal Typicality and Dynamical Typicality for a Random Block-Band Matrix Model

László Erdős, Joscha Henheik, Cornelia Vogel

We prove normal typicality and dynamical typicality for a (centered) random block-band matrix model with block-dependent variances. A key feature of our model is that we achieve in…

math.PR2024

Cusp Universality for Correlated Random Matrices

László Erdős, Joscha Henheik, Volodymyr Riabov

For correlated real symmetric or complex Hermitian random matrices, we prove that the local eigenvalue statistics at any cusp singularity are universal. Since the density of states…

math.PR2024

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…

math-ph2024

Loschmidt Echo for Deformed Wigner Matrices

László Erdős, Joscha Henheik, Oleksii Kolupaiev

We consider two Hamiltonians that are close to each other, $H_{1} \approx H_{2}$ , and analyze the time-decay of the corresponding Loschmidt echo $\mathfrak{M}(t) := |\langle ψ_0, \mat…

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…

math.PR2024★ 1 cited

Eigenstate Thermalization Hypothesis for Wigner-type Matrices

Volodymyr Riabov, László Erdős

We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for observa…

math-ph2023★ 2 cited

Prethermalization for Deformed Wigner Matrices

László Erdős, Joscha Henheik, Jana Reker +1

We prove that a class of weakly perturbed Hamiltonians of the form $H_{λ} = H_{0} + λW$ , with $W$ being a Wigner matrix, exhibits prethermalization. That is, the time evolution generate…

math.PR2023

Density of Brown measure of free circular Brownian motion

László Erdős, Hong Chang Ji

We consider the Brown measure of the free circular Brownian motion, $a + t x$ , with an arbitrary initial condition $a$ , i.e. $\boldsymbol…

math.PR2023★ 1 cited

Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices

László Erdős, Hong Chang Ji

We consider $N \times N$ non-Hermitian random matrices of the form $X + A$ , where $A$ is a general deterministic matrix and $N X$ consists of independent entries with zero mean,…

math.PR2022★ 1 cited

Mesoscopic Central Limit Theorem for non-Hermitian Random Matrices

Giorgio Cipolloni, László Endős, Dominik Schröder

We prove that the mesoscopic linear statistics $\sum_{i} f (n^{a} (σ_{i} - z_{0}))$ of the eigenvalues ${σ_{i}}_{i}$ of large $n \times n$ non-Hermitian random matrices with complex centred i.i.d…

math.PR2022

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 $n \times n$ random matrix with independent id…

math.PR2021

Functional CLT for non-Hermitian random matrices

László Erdős, Hong Chang Ji

For large dimensional non-Hermitian random matrices $X$ with real or complex independent, identically distributed, centered entries, we consider the fluctuations of $f (X)$ as a mat…

math.PR2021

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…

math.PR2021

Small deviation estimates for the largest eigenvalue of Wigner matrices

László Erdős, Yuanyuan Xu

We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables…

math.PR2021★ 6 cited

Dynamics of a rank-one perturbation of a Hermitian matrix

Guillaume Dubach, László Erdős

We study the eigenvalue trajectories of a time dependent matrix $G_{t} = H + i t v v^{*}$ for $t \geq 0$ , where $H$ is an $N \times N$ Hermitian random matrix and $v$ is a unit vector. I…

math.PR2021

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 $N \times N$ Wigner matrix and prove that it has Gaussian fluctuation for each bulk eigenv…

math.PR2020★ 1 cited

Functional Central Limit Theorems for Wigner Matrices

Giorgio Cipolloni, László Erdős, Dominik Schröder

We consider the fluctuations of regular functions $f$ of a Wigner matrix $W$ viewed as an entire matrix $f (W)$ . Going beyond the well studied tracial mode, $Tr [f (W)]$ , whi…

math.PR2020

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 $X$ with independent, iden…

math.PR2019

Randomly coupled differential equations with elliptic correlations

László Erdős, Torben Krüger, David Renfrew

We consider the long time asymptotic behavior of a large system of $N$ linear differential equations with random coefficients. We allow for general elliptic correlation structures…

math.PR2016★ 1 cited

Local single ring theorem on optimal scale

Zhigang Bao, László Erdős, Kevin Schnelli

Let $U$ and $V$ be two independent $N$ by $N$ random matrices that are distributed according to Haar measure on $U (N)$ . Let $Σ$ be a non-negative deterministic $N$ by $N$ matrix. T…

math-ph2014★ 105 cited

Phase Transition in the Density of States of Quantum Spin Glasses

László Erdős, Dominik Schröder

We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared wi…