@article{12148,
abstract = {We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables.},
author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J},
issn = {2050-5094},
journal = {Forum of Mathematics, Sigma},
keywords = {Computational Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics, Statistics and Probability, Algebra and Number Theory, Theoretical Computer Science, Analysis},
publisher = {Cambridge University Press},
title = {{Rank-uniform local law for Wigner matrices}},
doi = {10.1017/fms.2022.86},
volume = {10},
year = {2022},
}