# Normal fluctuation in quantum ergodicity for Wigner matrices

@article{Cipolloni2022NormalFI,
title={Normal fluctuation in quantum ergodicity for Wigner matrices},
author={Giorgio Cipolloni and L'aszl'o ErdHos and Dominik Schroder},
journal={The Annals of Probability},
year={2022}
}
• Published 11 March 2021
• Mathematics
• The Annals of Probability
We consider the quadratic form of a general deterministic matrix on the eigenvectors of an N×N Wignermatrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the largeN limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by [24] and our recent multi-resolvent local laws [11].
8 Citations

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