论文标题
关于频谱平均和随机schrödinger操作员的局部密度的一些评论，$ l^2（r^d）$
Some remarks on spectral averaging and the local density of states for random Schrödinger operators on $L^2 ( R^d )$
论文作者
论文摘要
我们证明了一些局部估计值，用于随机Schrödinger操作员的光谱投影仪，仅限于立方体$λ\子集r^d $。我们还提供了基于分析扰动理论的光谱平均结果的新证明。共同，这些提供了韦格纳估计的另一个证明，并具有明确形式的常数和替代证明Birman-Solomyak公式。我们还使用这些结果来证明局部状态密度的Lipschitz连续性在限制的随机schrödingeroperators上的限制性家族$λ\ subset r^d $，以$ d \ geq 1 $。该结果适用于没有定位假设的低能量，但不足以扩展到无限体积的极限。
We prove some local estimates on the trace of spectral projectors for random Schrödinger operators restricted to cubes $Λ\subset R^d$. We also present a new proof of the spectral averaging result based on analytic perturbation theory. Together, these provide another proof of the Wegner estimate with an explicit form of the constant and an alternate proof of the Birman-Solomyak formula. We also use these results to prove the Lipschitz continuity of the local density of states function for a restricted family of random Schrödinger operators on cubes $Λ\subset R^d$, for $d \geq 1$. The result holds for low energies without a localization assumption but is not strong enough to extend to the infinite-volume limit.
