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
Cipolloni, G., Erdős, L., Schroeder, D. (2022). Normal fluctuation in quantum ergodicity for Wigner matrices. ANNALS OF PROBABILITY, 50(3), 984-1012 [10.1214/21-AOP1552].
Normal fluctuation in quantum ergodicity for Wigner matrices
Cipolloni, Giorgio;
2022-01-01
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 lawsFile in questo prodotto:
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