Abstract
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.
Original language | English |
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Pages (from-to) | 2887-2893 |
Number of pages | 7 |
Journal | Proceedings of the American Mathematical Society |
Volume | 136 |
Issue number | 8 |
DOIs | |
State | Published - Aug 2008 |
Keywords
- Integrated density of states
- Lower bound
- Random Schrödinger operators
- Wegner estimate
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics