Abstract
We prove that the linear statistics of the eigenvalues of a Wigner matrix converge to a universal Gaussian process on all mesoscopic spectral scales, that is, scales larger than the typical eigenvalue spacing and smaller than the global extent of the spectrum.
| Original language | English |
|---|---|
| Pages (from-to) | 1510-1550 |
| Journal | Annals of Applied Probability |
| Volume | 27 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Jun 2017 |
| Externally published | Yes |
Research Keywords
- linear statistics
- mesoscopic eigenvalue distribution
- Universality
- Wigner matrices
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