An isoperimetric inequality on the ℓp balls
The normalised volume measure on the unit ball (1≤≤2) satisfies the following isoperimetric inequality: the boundary measure of a set of measure is at least log(1/), where =min(, 1−).
Localisation for non-monotone Schrödinger operators
We study localisation effects of strong disorder on the spectral and dynamical properties of (matrix and scalar) Schrödinger operators with non-monotone random potentials, on the -dimensional lattice. Our results include dynamical localisation, i.e. exponentially decaying bounds on the transition amplitude in the mean. They are derived through the study of fractional moments of the resolvent, which are finite due to resonance-diffusing effects of the disorder. One of the byproducts of the analysis...
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