arXiv Open Access 2022

Rank-uniform local law for Wigner matrices

Giorgio Cipolloni László Erdős Dominik Schröder

Lihat Sumber

Abstrak

We prove a general local law for Wigner matrices which optimally handles observables of arbitrary rank and thus it unifies the well-known averaged and isotropic local laws. As an application, we prove that the quadratic forms of a general deterministic matrix $A$ on the bulk eigenvectors of a Wigner matrix has approximately Gaussian fluctuation. For the bulk spectrum, we thus generalize our previous result [arXiv:2103.06730] valid for test matrices $A$ of large rank as well as the result of Benigni and Lopatto [arXiv:2103.12013] valid for specific small rank observables.

Topik & Kata Kunci

math.PR

Penulis (3)

Giorgio Cipolloni

László Erdős

Dominik Schröder

Format Sitasi

APA MLA BibTeX

Cipolloni, G., Erdős, L., Schröder, D. (2022). Rank-uniform local law for Wigner matrices. https://arxiv.org/abs/2203.01861

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓