论文标题
Toeplitz矩阵的光谱统计
Spectral statistics of Toeplitz matrices
论文作者
论文摘要
数值研究了具有独立分布元件的遗传学随机toeplitz矩阵的光谱统计。发现复杂的toeplitz矩阵的特征值统计数据令人惊讶地吻合了在某些伪综合台球中观察到的中等型统计的半频道分布。中间行为的起源可以归因于以下事实：傅立叶变换的随机toeplitz矩阵在主对角线之外具有与关键随机矩阵集合的慢速衰减。具有I.I.D的真实随机toeplitz矩阵的全频谱的统计特性。元素接近泊松分布，但它们的每个构成子谱又被半峰分布很好地描述了。这些发现在中级统计数据中开放了新的观点。
Spectral statistics of hermitian random Toeplitz matrices with independent identically distributed elements is investigated numerically. It is found that the eigenvalue statistics of complex Toeplitz matrices is surprisingly well approximated by the semi-Poisson distribution belonging to intermediate-type statistics observed in certain pseudo-integrable billiards. The origin of intermediate behaviour could be attributed to the fact that Fourier transformed random Toeplitz matrices have the same slow decay outside the main diagonal as critical random matrix ensembles. The statistical properties of the full spectrum of real random Toeplitz matrices with i.i.d. elements are close to the Poisson distribution but each of their constituted sub-spectra is again well described by the semi-Poisson distribution. The findings open new perspective in intermediate statistics.
