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Fluctuations in local quantum unique ergodicity for generalized Wigner matrices
- Publication Year :
- 2021
-
Abstract
- We study the eigenvector mass distribution for generalized Wigner matrices on a set of coordinates $I$, where $N^\varepsilon \le | I | \le N^{1- \varepsilon}$, and prove it converges to a Gaussian at every energy level, including the edge, as $N\rightarrow \infty$. The key technical input is a four-point decorrelation estimate for eigenvectors of matrices with a large Gaussian component. Its proof is an application of the maximum principle to a new set of moment observables satisfying parabolic evolution equations. Additionally, we prove high-probability Quantum Unique Ergodicity and Quantum Weak Mixing bounds for all eigenvectors and all deterministic sets of entries using a novel bootstrap argument.<br />Comment: 44 pages. Minor revisions
- Subjects :
- Mathematics - Probability
Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2103.12013
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00220-022-04314-z