TY - JOUR
AB - 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.
AU - Cipolloni, Giorgio
AU - Erdös, László
AU - Schröder, Dominik J
ID - 12148
JF - Forum of Mathematics, Sigma
KW - Computational Mathematics
KW - Discrete Mathematics and Combinatorics
KW - Geometry and Topology
KW - Mathematical Physics
KW - Statistics and Probability
KW - Algebra and Number Theory
KW - Theoretical Computer Science
KW - Analysis
SN - 2050-5094
TI - Rank-uniform local law for Wigner matrices
VL - 10
ER -