The proposed approach complements the classical Wegner estimate which says that the IDS in the short-range models is at least as regular as the marginal distribution of the disorder. In the models with non-local interaction the finite-volume IDS is much more regular than the underlying disorder. In turn, smoothness of the finite-volume IDS is responsible for a mechanism complementing the Lifshitz tails phenomenon.

The new eigenvalue concentration estimates give rise to relatively simple proofs of Anderson localization in several classes of discrete and continuous long-range models with arbitrarily singular disorder. The present paper addresses the model with power-law decay of the potential.

提出的方法是对经典Wegner估计的补充，该估计称，短程模型中的IDS至少与疾病的边缘分布一样规则。在具有非局部相互作用的模型中，有限体积的IDS比潜在的疾病更规则。反过来，有限体积IDS的平滑度是补充Lifshitz尾巴现象的机制的原因。

新的特征值集中估计在具有任意奇异性障碍的几类离散和连续远程模型中产生了相对简单的Anderson定位证明。本文用电势的幂律衰减来解决该模型。