• Corpus ID: 248006360

Almost-optimal bulk regularity conditions in the CLT for Wigner matrices

@inproceedings{Landon2022AlmostoptimalBR,
  title={Almost-optimal bulk regularity conditions in the CLT for Wigner matrices},
  author={Benjamin Landon and Philippe Sosoe},
  year={2022}
}
We consider linear spectral statistics of the form $\mathrm{tr} ( \varphi (H))$ for test functions $\varphi$ of low regularity and Wigner matrices $H$ with smooth entry distribution. We show that for functions $\varphi$ in the Sobolev space $H^{1/2+\varepsilon}$ or the space $C^{1/2+\varepsilon}$, that are supported within the spectral bulk of the semicircle distribution, these linear spectral statistics have asymptotic Gaussian fluctuations with the same variance as in the CLT for functions of…