A lower bound for the density of states of the lattice Anderson model
A lower bound for the density of states of the lattice Anderson model
复制标题
晶格安德森模型态密度的下界
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
P. Muller
中科院分区：
文献类型：
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作者：
P. Hislop;P. Muller
考虑多维立方晶格上的安德森模型，在一定条件下证明了态密度的一个正下界。例如，如果随机变量是独立同分布的，并且概率测度有一个紧支撑的有界Lebesgue密度，并且如果这个密度在其支撑上本质上是有界的，那么我们证明了对于Lebesgue-几乎确定性谱中的每一个能量，状态密度都是严格正的。
We consider the Anderson model on the multi-dimensional cubic lattice and prove a positive lower bound on the density of states under certain conditions. For example, if the random variables are independently and identically distributed and the probability measure has a bounded Lebesgue density with compact support, and if this density is essentially bounded away from zero on its support, then we prove that the density of states is strictly positive for Lebesgue-almost every energy in the deterministic spectrum.