关于相依加权随机带矩阵
On Weighted Random Band-Matrices with Dependences
摘要：
我们开发的技术来计算随机矩阵M的特征值统计量的k阶矩，其条目不一定是独立的。依赖性通过M的条目对上的等价关系来控制。此外，这些元素是加权的，这意味着它们与（0，1）上的黎曼可积函数相乘。最后讨论了特征值统计量依概率的弱收敛性，不仅讨论了加权矩阵，而且讨论了带宽为o（N）的带矩阵。
英文摘要：
We develop techniques to compute the k-th Moment of the Eigenvalue-statistic for a random Matrix M the entries of which do not have to be necessarily Independent. The dependence is controlled via an equivalence relation on the pairs of the entries of M. Furthermore the entries are weighted, that means they are multiplied with a Riemann-integrable function on (0,1). Finally also weak convergence in probability of the Eigenvalue statsitic is discussed not for the weighted Matrix but also for band matrices the band-width of which behaves like o(N).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
