Smoothness of the Integrated Density of States for Random Schrödinger Operators on Multidimensional Strips

• Main Author: Glaffig, Clemens H.
• Format: Others
• Published: 1988
• Online Access: https://thesis.library.caltech.edu/3307/4/Glaffig_ch_1988.pdf; Glaffig, Clemens H. (1988) Smoothness of the Integrated Density of States for Random Schrödinger Operators on Multidimensional Strips. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4GBV-RA25. https://resolver.caltech.edu/CaltechETD:etd-09012005-155238 <https://resolver.caltech.edu/CaltechETD:etd-09012005-155238>

<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>