Smoothness of the Integrated Density of States for Random Schrödinger Operators on Multidimensional Strips
<p>We investigate smoothness properties of the integrated density of states (ids) for random Schrödinger operators on a multidimensional strip lattice, where only the potentials on the "top surface" of this lattice have a distribution with some regularity.</p> <p>We vi...
| Summary: | <p>We investigate smoothness properties of the integrated density of states (ids) for random Schrödinger operators on a multidimensional strip lattice, where only the potentials on the "top surface" of this lattice have a distribution with some regularity.</p>
<p>We view the eigenvalue equation on the strip as the action of an abstract group on some homogeneous space, from where we derive a representation of the ids in terms of a distinguished measure on that homogeneous space.</p>
<p>This representation allows us to conclude that using minimal smoothness of the potential distribution on the "top surface", combined with a negative moment condition for the distribution of all other potentials, is enough to obtain smoothness of the ids. This includes the original Anderson model.</p>
<p>We also discuss cases, where the distribution of the potentials below the "top surface" is Bernoulli, satisfying this negative moment condition.</p> |
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