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Matthias Täufer, Ivan Veselić: Conditional Wegner estimate for the standard random breather potential

Matthias Täufer, Ivan Veselić: Conditional Wegner estimate for the standard random breather potential


Author(s):
Matthias Täufer
Ivan Veselić
Title:
Matthias Täufer, Ivan Veselić: Conditional Wegner estimate for the standard random breather potential
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 07, 2014
Mathematics Subject Classification:
    60H25 []
    35J10 []
Abstract:
We prove a conditional Wegner estimate for Schr\"odinger operators with random potentials of breather type. More precisely, we reduce the proof of the Wegner estimate to a scale free unique continuation principle. The relevance of such unique continuation principles has been emphasized in previous papers, in particular in recent years. We consider the \emph{standard} breather model, meaning that the single site potential is the characteristic function of a ball or a cube. While our methods work for a substantially larger class of random breather potentials, we discuss in this particular paper only the standard model in order to make the arguments and ideas easily accessible.
Keywords:

Language:
English
Publication time:
06/2014

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