Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrices and sample covariance matrices
| Autor: | Kevin Schnelli, Yuanyuan Xu, Yiting Li |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Characteristic function (probability theory) Probability (math.PR) Hermitian matrix Matrix (mathematics) Bounded function Diagonal matrix Statistics FOS: Mathematics Statistics Probability and Uncertainty Random matrix Eigenvalues and eigenvectors Mathematics - Probability 15B52 60B20 Central limit theorem Mathematics |
| Popis: | We consider $N$ by $N$ deformed Wigner random matrices of the form $X_N=H_N+A_N$, where $H_N$ is a real symmetric or complex Hermitian Wigner matrix and $A_N$ is a deterministic real bounded diagonal matrix. We prove a universal Central Limit Theorem for the linear eigenvalue statistics of $X_N$ for all mesoscopic scales both in the spectral bulk and at regular edges where the global eigenvalue density vanishes as a square root. The method relies on the characteristic function method in [47], local laws for the Green function of $X_N$ in [3, 46, 51] and analytic subordination properties of the free additive convolution [24, 41]. We also prove the analogous results for high-dimensional sample covariance matrices. Final version |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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