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Generic sets in spaces of measures and generic singular continuous spectrum for Delone Hamiltonians
Daniel Lenz and Peter Stollmann
Source: Duke Math. J. Volume 131, Number 2
(2006), 203-217.
Abstract
We show that geometric disorder leads to some purely singular continuous spectrum generically. The main input is a result of Simon known as the Wonderland theorem in [17, Section 2]. Here we provide an alternative approach and actually a slight strengthening by showing that various sets of measures defined by regularity properties are generic in the set of all measures on a locally compact metric space. As a byproduct, we obtain the fact that a generic measure on euclidean space is singular continuous
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1137077883
Digital Object Identifier: doi:10.1215/S0012-7094-06-13121-6
Mathematical Reviews number (MathSciNet): MR2219240
Zentralblatt MATH identifier: 1103.81017
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