论文标题
基于Wigner的猜想，在随机矩阵理论中的高阶级别间距
Higher-order level spacings in random matrix theory based on Wigner's conjecture
论文作者
论文摘要
高阶高间距的分布，即$ \ {s_ {i}^{（n）} = e_ {i+n} -e_ {i+n} -e_ {i} \} $，$ n \ geq 1 $是在分析上使用wigner类似的surmise for Gaussian Ensembles antrantically在分析上得出的。在高斯合奏中发现了$ s^{（n）} $遵循广泛的Wigner-dyson分布，其重新缩放参数$α=νc_{n+1}^2+n-1 $，而Poisson Ensemble中的complesemble则遵循了index $ n $ n $ n $ n $ n $ n $ n $ n $。通过模拟随机自旋系统以及Riemann Zeta函数的非平凡零来提供数值证据。还讨论了差距比的高阶概括。
The distribution of higher order level spacings, i.e. the distribution of $\{s_{i}^{(n)}=E_{i+n}-E_{i}\}$ with $n\geq 1$ is derived analytically using a Wigner-like surmise for Gaussian ensembles of random matrix as well as Poisson ensemble. It is found $s^{(n)}$ in Gaussian ensembles follows a generalized Wigner-Dyson distribution with rescaled parameter $α=νC_{n+1}^2+n-1$, while that in Poisson ensemble follows a generalized semi-Poisson distribution with index $n$. Numerical evidences are provided through simulations of random spin systems as well as non-trivial zeros of Riemann zeta function. The higher order generalizations of gap ratios are also discussed.
