@article{11418, 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).}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {2168-894X}, journal = {Annals of Probability}, number = {3}, pages = {984--1012}, publisher = {Institute of Mathematical Statistics}, title = {{Normal fluctuation in quantum ergodicity for Wigner matrices}}, doi = {10.1214/21-AOP1552}, volume = {50}, year = {2022}, }