Oleksii Kolupaiev

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20212026

most citedAnomalous singularity of the solution of the vector Dyson equation in the critical case

2 citations · 3 across the 8 of their papers we have counts for

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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.PR2026

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…

math.PR2026

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…

math.PR2025

Spectral independence of almost fully correlated random matrices

Oleksii Kolupaiev

We study the joint spectral properties of two coupled random matrices $H^{(1)}$ and $H^{(2)}$ , which are either real symmetric or complex Hermitian. The entries of these matrices e…

math.PR2025

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…

math.PR2025

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…

math.PR2024

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.PR2021★ 2 cited

Anomalous singularity of the solution of the vector Dyson equation in the critical case

Oleksii Kolupaiev

We consider the solution of the vector Dyson equation $- 1/ m = z + S m$ in the case when $S$ has a block staircase structure with $(n - 1)$ different critical zero blocks below the strictl…