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Uncertainty relations and Wegner estimates for random breather potentials

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Periodic and Ergodic Spectral Problems

Co-authors: Ivica Nakic (Zagreb University), Matthias Tufer (TU Chemnitz), Martin Tautenhahn (TU Chemnitz)

We present a new scale-free, quantitative unique continuation estimate for Schroedinger operators in multidimensional space. Depending on the context such estimates are sometimes called uncertainty relations, observations inequalities or spectral inequalities. To illustrate its power we prove a Wegner estimate for Schroedinger operators with random breather potentials. Here we encounter a non-linear dependence on the random coupling constants, preventing the use of standard perturbation theory. The proofs rely on an analysis of the level sets of the random potential, and can be extended to a rather general framework.

This talk is part of the Isaac Newton Institute Seminar Series series.

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