论文标题
具有方差曲线的最大矩阵特征值的巨大偏差
Large deviations for the largest eigenvalue of matrices with variance profiles
论文作者
论文摘要
在本文中，我们考虑具有差异配置文件（也称为wigner-type矩阵）的Wigner矩阵，其形式为$ x_n（i，j）=σ（i/n，j/n，j/n，j/n）a_ {i，j}/j}/j}/j}/\ sqrt {n} $ n $σ$ syment syment protical the $ nece $ nece $ neat $ 2 $ 2 $ 2 $ 2 $ 2]分段常数。我们证明了这些矩阵最大的特征值在相同的尖锐次高斯界限的情况下以及对$σ$的其他一些假设的大偏差原理。例如，$ [ - \ sqrt {3}，\ sqrt {3}] $上的高斯变量，rademacher变量或统一变量进行了验证。
In this article we consider Wigner matrices $X_N$ with variance profiles (also called Wigner-type matrices) which are of the form $X_N(i,j) = σ(i/N,j/N) a_{i,j} / \sqrt{N}$ where $σ$ is a symmetric real positive function of $[0,1]^2$ and $σ$ will be taken either continuous or piecewise constant. We prove a large deviation principle for the largest eigenvalue of those matrices under the same condition of sharp sub-Gaussian bound and for some other assumptions on $σ$. These sub-Gaussian bounds are verified for example for Gaussian variables, Rademacher variables or uniform variables on $[- \sqrt{3}, \sqrt{3}]$.
