Ivan Veselić, Martin Tautenhahn: A note on regularity for discrete alloy-type models II

Author(s):

Ivan Veselić
Martin Tautenhahn

Title:

Ivan Veselić, Martin Tautenhahn: A note on regularity for discrete alloy-type models II

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 02, 2013

Mathematics Subject Classification:

60G10	[]
60G30	[]
60G50	[]
82B44	[]

Abstract:

Alloy-type potentials on the lattice ℤ^d give rise to a correlated random field. Depending on the regularity properties of the conditional distributions (or conditional densities --- if they exist) standard methods developed for the i.i.d. Anderson model can be applied or not. This refers to Wegner estimates, fractional moment bounds, Minami estimates, and other estimates obtained by averaging procedures. In [5] we studied a (quite large) class of alloy-type potentials on the lattice ℤ and showed that certain conditional probabilities exhibit a bad behavior. Consequently, a regularity condition spelled out in [1] is not satisfied in this case. We revisit in this note the question of regularity properties of the conditional distribution of the potential values and discuss certain consequences for the recent preprint [4].

Keywords:

Language:

English

Publication time:

01/2013