Rank-uniform local law for Wigner matrices Cipolloni, Giorgio ; https://orcid.org/0000-0002-4901-7992 Erdös, László ; https://orcid.org/0000-0001-5366-9603 Schröder, Dominik J ; https://orcid.org/0000-0002-2904-1856 Computational Mathematics Discrete Mathematics and Combinatorics Geometry and Topology Mathematical Physics Statistics and Probability Algebra and Number Theory Theoretical Computer Science Analysis ddc:510 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. Cambridge University Press 2022 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/12148 https://research-explorer.ista.ac.at/download/12148/12356 Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href="https://doi.org/10.1017/fms.2022.86">10.1017/fms.2022.86</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1017/fms.2022.86 info:eu-repo/semantics/altIdentifier/issn/2050-5094 info:eu-repo/semantics/altIdentifier/wos/000873719200001 info:eu-repo/semantics/openAccess