Normal fluctuation in quantum ergodicity for Wigner matrices
Giorgio Cipolloni, László Erdős, Dominik Schröder
Abstract
We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N×N Wigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021) 1005–1048).
Topics & Concepts
MathematicsErgodicityEigenvalues and eigenvectorsBrownian motionGaussianRandom matrixLimit (mathematics)Quadratic equationMathematical physicsRank (graph theory)Matrix (chemical analysis)Pure mathematicsQuantumWigner distribution functionMathematical analysisCombinatoricsQuantum mechanicsStatisticsPhysicsComposite materialMaterials scienceGeometryRandom Matrices and ApplicationsQuantum many-body systemsQuantum Information and Cryptography