Uniform single- and two-resolvent local laws for arbitrary deformations of Wigner matrices yield ETH and localization profiles for all λ and H0.
Almost optimal bulk regularity conditions in the CLT for Wigner matrices
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
abstract
We consider linear spectral statistics of the form $\mathrm{tr} ( \varphi (H))$ for test functions $\varphi$ of low regularity and Wigner matrices $H$ with smooth entry distribution. We show that for functions $\varphi$ in the Sobolev space $H^{1/2+\varepsilon}$ or the space $C^{1/2+\varepsilon}$, that are supported within the spectral bulk of the semicircle distribution, these linear spectral statistics have asymptotic Gaussian fluctuations with the same variance as in the CLT for functions of higher regularity, for any $\varepsilon >0$.
representative citing papers
Establishes full LDPs for the largest eigenvalue of sub-Gaussian Wigner matrices via finite-N approximation by restricted annealed free energies, identifying a transition from GOE rate function to non-universal rate at the onset of eigenvector localization.
Mesoscopic CLT for linear eigenvalue statistics of correlated Hermitian matrices, via multivariate cumulant expansion, multi-resolvent local laws, and operator-level variance-kernel analysis.
Variance of mesoscopic linear spectral statistics for random quantum graphs coincides with GOE/GUE.
For smooth Wigner matrices the log-determinant and eigenvalue counting fields converge in law to centered Gaussian, logarithmically correlated random elements in every negative Sobolev space H^{-s}.
citing papers explorer
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On a Rosenzweig-Porter-type model
Uniform single- and two-resolvent local laws for arbitrary deformations of Wigner matrices yield ETH and localization profiles for all λ and H0.
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Full large deviation principles for the largest eigenvalue of sub-Gaussian Wigner matrices
Establishes full LDPs for the largest eigenvalue of sub-Gaussian Wigner matrices via finite-N approximation by restricted annealed free energies, identifying a transition from GOE rate function to non-universal rate at the onset of eigenvector localization.
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Mesoscopic eigenvalue statistics for correlated random matrices
Mesoscopic CLT for linear eigenvalue statistics of correlated Hermitian matrices, via multivariate cumulant expansion, multi-resolvent local laws, and operator-level variance-kernel analysis.
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Mesoscopic Linear Statistics for Two Ensembles of Quantum Graphs
Variance of mesoscopic linear spectral statistics for random quantum graphs coincides with GOE/GUE.
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Sobolev convergence of log-determinants for smooth Wigner matrices
For smooth Wigner matrices the log-determinant and eigenvalue counting fields converge in law to centered Gaussian, logarithmically correlated random elements in every negative Sobolev space H^{-s}.