Initial length scale estimate for waveguides with some random singular potentials

Authors

  • D.I. Borisov
    University of Hradec Králové, Rokitanskeho, 62, 50003, Hradec Králové, Czech Republic
    Bashkir State Pedagogical University named after M. Akhmulla, October rev. st., 3a, 450000, Ufa, Russia
    Institute of Mathematics CC USC RAS, Chernyshevskii str., 112, 450008, Ufa, Russia
  • R.Kh. Karimov
    Bashkir State Pedagogical University named after M. Akhmulla, October rev. st., 3a, 450000, Ufa, Russia
  • T.F. Sharapov
    Bashkir State Pedagogical University named after M. Akhmulla, October rev. st., 3a, 450000, Ufa, Russia

DOI:

https://doi.org/10.13108/2015-7-2-33

Keywords:

random operator, initial length scale estimate, perturbation, small parameter, spectral localization.

Abstract

In this work we consider three examples of random singular perturbations in multi-dimensional models of waveguides. These perturbations are described by a large potential supported on a set of a small measure, by a compactly supported fast oscillating potential, and by a delta-potential. In all cases we prove initial length scale estimate.

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Published

20.06.2015

Issue

Vol. 7 No. 2 (2015): Ufa Mathematical Journal 2015, volume 7 , issue 2

Section

Article