Mesoscopic linear statistics of Wigner matrices
| Autor: | Lodhia, A., Simm, N. J. |
|---|---|
| Rok vydání: | 2015 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study linear spectral statistics of $N \times N$ Wigner random matrices $\mathcal{H}$ on mesoscopic scales. Under mild assumptions on the matrix entries of $\mathcal{H}$, we prove that after centering and normalizing, the trace of the resolvent $\mathrm{Tr}(\mathcal{H}-z)^{-1}$ converges to a stationary Gaussian process as $N \to \infty$ on scales $N^{-1/3} \ll \mathrm{Im}(z) \ll 1$ and explicitly compute the covariance structure. The limit process is related to certain regularizations of fractional Brownian motion and logarithmically correlated fields appearing in \cite{FKS13}. Finally, we extend our results to general mesoscopic linear statistics and prove that the limiting covariance is given by the $H^{1/2}$-norm of the test functions. Comment: 32 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|