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- W1499525344 abstract "In this paper, we study the fluctuation of linear eigenvalue statistics of Random Band Matrices defined by $M_{n}=frac{1}{sqrt{b_{n}}}W_{n}$, where $W_{n}$ is a $ntimes n$ band Hermitian random matrix of bandwidth $b_{n}$, i.e., the diagonal elements and only first $b_{n}$ off diagonal elements are nonzero. Also variances of the matrix elmements are upto a order of constant. We study the linear eigenvalue statistics $mathcal{N}(phi)=sum_{i=1}^{n}phi(lambda_{i})$ of such matrices, where $lambda_{i}$ are the eigenvalues of $M_{n}$ and $phi$ is a sufficiently smooth function. We prove that $sqrt{frac{b_{n}}{n}}[mathcal{N}(phi)-mathbb{E} mathcal{N}(phi)]stackrel{d}{to} N(0,V(phi))$ for $b_{n}>>sqrt{n}$, where $V(phi)$ is given in the Theorem 1." @default.
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- W1499525344 date "2016-01-01" @default.
- W1499525344 modified "2023-09-23" @default.
- W1499525344 title "Fluctuations of Linear Eigenvalue Statistics of Random Band Matrices" @default.
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- W1499525344 doi "https://doi.org/10.1137/s0040585x97t987788" @default.
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