Monday, June 17, 2013

1306.3459 (Alexander Elgart et al.)

Eigenvalue statistics for random block operators    [PDF]

Alexander Elgart, Daniel Schmidt
We derive a criterion that allows us to establish an upper bound on the probability that a local Hamiltonian has at least $n$ eigenvalues in a given energy interval. Such an estimate is known as an n-level Wegner estimate. We demonstrate its usefulness by verifying the input conditions of our criterion for random block operators that arise in the Bogoliubov-de Gennes theory of dirty superconductors. This gives a usual (1-level) Wegner estimate for these operators, as well as a weakened Minami estimate.
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