带随机矩阵集成谱普适性的渐近展开与尺度
On Asymptotic Expansions and Scales of Spectral Universality in Band Random Matrix Ensembles
摘要：
本文考虑具有随机独立元素的N维实对称矩阵族H，其方差由函数U（（x-y）/b）确定.在（相对）窄带宽1<<b<<N的极限下，我们显式地得到了H的预解式的1/b-展开式的首项.导出的表达式表明，U（t）的衰减速率决定了本征值相关函数的泛值型的几个尺度。特别地，在U（t）= o（1/t^3）的情况下，得到了具有比率N/b^2的Altshuller-Shklovski渐近性。
英文摘要：
We consider the family of N-dimensional real symmetric matrices H with random independent entries whose variance is determined by a function U((x-y)/b). In the limit of (relatively) narrow band width 1<<b<<N, we obtain explicitly first terms of 1/b-expansion of the resolvent of H. The expressions derived show that the rate of decay of U(t) determines several scale of the universal form of the eigenvalue correlation function. In particular, in the case of U(t) = o(1/t^3), the Altshuller-Shklovski asymptotics with the ratio N/b^2 is obtained.
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。
