@article{19001,
  abstract     = {We consider two Hamiltonians that are close to each other, H1≈H2, and analyze the time-decay of the corresponding Loschmidt echo M(t):=|⟨ψ0,eitH2e−itH1ψ0⟩|2 that expresses the effect of an imperfect time reversal on the initial state ψ0. Our model Hamiltonians are deformed Wigner matrices that do not share a common eigenbasis. The main tools for our results are two-resolvent laws for such H1 and H2.},
  author       = {Erdös, László and Henheik, Sven Joscha and Kolupaiev, Oleksii},
  issn         = {1573-0530},
  journal      = {Letters in Mathematical Physics},
  publisher    = {Springer Nature},
  title        = {{Loschmidt echo for deformed Wigner matrices}},
  doi          = {10.1007/s11005-025-01904-5},
  volume       = {115},
  year         = {2025},
}

@unpublished{19546,
  abstract     = {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 deformed Wigner matrices $W+D_1$, $W+D_2$ and show
that their bulk eigenvectors become asymptotically orthogonal as soon as
$\mathrm{Tr}(D_1-D_2)^2\gg 1$, or their respective energies are separated on a
scale much bigger than the local eigenvalue spacing. Furthermore, we show that
quadratic forms of eigenvectors of $W+D_1$, $W+D_2$ with any deterministic
matrix $A\in\mathbf{C}^{N\times N}$ in a specific subspace of codimension one
are of size $N^{-1/2}$. This proves a generalization of the Eigenstate
Thermalization Hypothesis to eigenvectors belonging to two different spectral
families.},
  author       = {Cipolloni, Giorgio and Erdös, László and Henheik, Sven Joscha and Kolupaiev, Oleksii},
  booktitle    = {arXiv},
  title        = {{Eigenvector decorrelation for random matrices}},
  doi          = {10.48550/arXiv.2410.10718},
  year         = {2025},
}

@article{20478,
  abstract     = {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. The top eigenvalues of H^{(N)} and those of its immediate minor H^{(N-1)} are very strongly correlated, but this correlation becomes weaker for smaller minors H^{(N-k)} as k increases. For the GUE minor process the critical transition regime around k\sim N^{2/3} was analyzed by Forrester and Nagao (J. Stat. Mech.: Theory and Experiment, 2011) providing an explicit formula for the nontrivial joint correlation function. We prove that this formula is universal, i.e. it holds for the Wigner minor process. Moreover, we give a complete analysis of the sub- and supercritical regimes both for eigenvalues and for the corresponding eigenvector overlaps, thus we prove the decorrelation transition in full generality.},
  author       = {Bao, Zhigang and Cipolloni, Giorgio and Erdös, László and Henheik, Sven Joscha and Kolupaiev, Oleksii},
  issn         = {1432-2064},
  journal      = {Probability Theory and Related Fields},
  publisher    = {Springer Nature},
  title        = {{Decorrelation transition in the Wigner minor process}},
  doi          = {10.1007/s00440-025-01422-4},
  year         = {2025},
}

@article{14343,
  abstract     = {The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices. As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation.},
  author       = {Cipolloni, Giorgio and Erdös, László and Henheik, Sven Joscha and Kolupaiev, Oleksii},
  issn         = {2050-5094},
  journal      = {Forum of Mathematics, Sigma},
  publisher    = {Cambridge University Press},
  title        = {{Gaussian fluctuations in the equipartition principle for Wigner matrices}},
  doi          = {10.1017/fms.2023.70},
  volume       = {11},
  year         = {2023},
}