论文标题
一维随机施罗丁算子的特征值波动
Eigenvalue Fluctuations of 1-dimensional random Schrödinger operators
论文作者
论文摘要
作为Breuer，Grinshpon和White \ cite {B}的论文的扩展，我们研究了Schrödinger操作员特征值的线性统计数据，其随机衰减潜力随$ {\ cal o}的随机衰减潜力（\ cal O}（x^{ - α}）$（$α> 0 $）。 We first prove similar statements as in \cite{B} for the trace of $f(H)$, where $f$ belongs to a class of analytic functions : there exists a critical exponent $α_c$ such that the fluctuation of the trace of $f(H)$ converges in probability for $α> α_c$, and satisfies a CLT statement for $α\le α_c$, where $α_c$取决于$ f $。此外，我们研究其期望值的渐近行为。
As an extension to the paper by Breuer, Grinshpon, and White \cite{B}, we study the linear statistics for the eigenvalues of the Schrödinger operator with random decaying potential with order ${\cal O}(x^{-α})$ ($α>0$) at infinity. We first prove similar statements as in \cite{B} for the trace of $f(H)$, where $f$ belongs to a class of analytic functions : there exists a critical exponent $α_c$ such that the fluctuation of the trace of $f(H)$ converges in probability for $α> α_c$, and satisfies a CLT statement for $α\le α_c$, where $α_c$ differs depending on $f$. Furthermore we study the asymptotic behavior of its expectation value.
