Normal fluctuation in quantum ergodicity for Wigner matrices
نویسندگان
چکیده
We consider the quadratic form of a general high-rank deterministic matrix on eigenvectors an N×N Wigner and prove that it has Gaussian fluctuation for each bulk eigenvector in large N limit. The proof is combination energy method Dyson Brownian motion inspired by Marcinek Yau (2021) our recent multiresolvent local laws (Comm. Math. Phys. 388 1005–1048).
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ژورنال
عنوان ژورنال: Annals of Probability
سال: 2022
ISSN: ['0091-1798', '2168-894X']
DOI: https://doi.org/10.1214/21-aop1552