On Wegner bounds for one-dimensional multi-particle Bernoulli-Anderson models in the continuum

We prove the Wegner bounds for the one-dimensional interacting multi-particle Anderson models in the continuum. The results apply to singular probability distribution functions such as the Bernoulli's measures. The proofs need the amplitude of the inter-particle interaction potential to be sufficiently weak. As a consequence, the results imply the Anderson localization via the multi-scale analysis.

[1]  T. Ekanga.  Wegner bounds for N-body interacting Bernoulli-Anderson models in one dimension , 2016, 1612.08303.

[2]  T. Ekanga.  Anderson localization for weakly interacting multi-particle models in the continuum , 2016, 1611.10345.

[3]  T. Ekanga.  Multi-particle localization for weakly interacting Anderson tight-binding models , 2013, 1312.4180.

[4]  P. Hislop,et al.  Optimal Wegner estimate and the density of states for N-body, interacting Schrodinger operators with random potentials , 2013, 1310.6959.

[5]  T. Ekanga.  On two-particle Anderson localization at low energies , 2011, 1203.1207.

[6]  A. B. D. Monvel,et al.  Wegner-type Bounds for a Multi-particle Continuous Anderson Model with an Alloy-type External Potential , 2008, 0812.2621.

[7]  Werner Kirsch,et al.  An Invitation to Random Schr¨ odinger operators , 2007 .

[8]  Y. Suhov,et al.  Wegner Bounds for a Two-Particle Tight Binding Model , 2007, 0708.2056.

[9]  J. Bourgain,et al.  On localization in the continuous Anderson-Bernoulli model in higher dimension , 2005 .

[10]  D. Damanik,et al.  LOCALIZATION FOR ONE DIMENSIONAL, CONTINUUM, BERNOULLI-ANDERSON MODELS , 2000, math-ph/0010016.

[11]  A. Klein,et al.  A new proof of localization in the Anderson tight binding model , 1989 .

[12]  René Carmona,et al.  Anderson localization for Bernoulli and other singular potentials , 1987 .

[13]  F. Wegner.  Bounds on the density of states in disordered systems , 1981 .

[14]  Peter Stollmann,et al.  Caught by disorder , 2001 .

[15]  R. Carmona,et al.  Spectral Theory of Random Schrödinger Operators , 1990 .