论文标题
结构化随机矩阵的统计特性
Statistical properties of structured random matrices
论文作者
论文摘要
研究了具有独立分布的条目的Hermitian Toeplitz，Hankel和Toeplitz-Plus-hankel随机矩阵的光谱特性。结合数值和分析论点，证明所有这些随机矩阵的光谱统计均具有中间类型，其特征是（i）在较小距离处的水平排斥，（ii）在较大距离处最近邻米分布的指数下降，（iii）不繁琐的频谱可压度的不繁琐的污垢（III）的差异（iii）的差异。傅立叶空间。我们的发现表明，与迄今为止所考虑的中间类型统计数据更加普遍和普遍，并在随机矩阵理论中打开了一个新的方向。
Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical and analytic arguments it is demonstrated that spectral statistics of all these random matrices is of intermediate type, characterized by (i) level repulsion at small distances, (ii) an exponential decrease of the nearest-neighbor distributions at large distances, (iii) a non-trivial value of the spectral compressibility, and (iv) the existence of non-trivial fractal dimensions of eigenvectors in Fourier space. Our findings show that intermediate-type statistics is more ubiquitous and universal than was considered so far and open a new direction in random matrix theory.
