Abstract
We consider operators with random potentials on graphs, such as the lattice version of the random Schrödinger operator. The main result is a general bound on the probabilities of simultaneous occurrence of eigenvalues in specified distinct intervals, with the corresponding eigenfunctions being separately localized within prescribed regions. The bound generalizes the Wegner estimate on the density of states. The analysis proceeds through a new multi-parameter spectral averaging principle.
Original language | English (US) |
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Article number | 045201 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 42 |
Issue number | 4 |
DOIs | |
State | Published - 2009 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)