论文标题
随机带GOE矩阵的波动和定位长度
Fluctuations and localization length for random band GOE matrix
论文作者
论文摘要
我们证明，goe随机频段矩阵本地化长度为$ \ le c \ left（\ log w \ right）^3 w^2 $，其中$ w $是频段的宽度，$ c $是绝对常数。我们的方法包括绿色函数边缘到边缘向量的动作方法，用于Schenker方法。这允许将动作分开和解除，以使\ emph {两个连续的Schur的大小互补的矢量动作的大小不能大于绝对常数}，从而变得透明。这是该方法的核心技术成分。它来自相当涉及的估计$（$ $的Metod $）$的主要估计值，以及一个方程式，将两个方程式相关。我们称之为后者\ emph {recurrence方程}。该方法导致\ emph {$ \ log $ - $ \ gtrsim nw^{ - 1} $}的vector Action的差异的下限，其中$ n $是goe块的总数，条件$ n \ lyssim w^d $，具有绝对常数$ d \ gg d \ gg 1 $ applies。
We prove that GOE random band matrix localization length is $\le C\left(\log W\right)^3 W^2$, where $W$ is the width of the band and $C$ is an absolute constant. Our method consists of Green function edge-to-edge vector action approach to the Schenker method. That allows to split and decouple the action, so that it becomes transparent that \emph{the magnitudes of two consecutive Schur complements vector actions can not be both larger than an absolute constant}. That is the central technological ingedient of the method. It comes from rather involved estimates $($ the main estimates of the metod $)$, in combination with an equation relating two magnitudes in question. We call the latter \emph{recurrence equation}. The method results in the \emph{lower bound of the variance of the $\log$--norm of the vector action at $\gtrsim NW^{-1}$}, where $N$ is the total number of GOE blocks, condition $N\lesssim W^D$ with an absolute constant $D\gg 1$ applies.
