Lifshitz Tails for Random Diagonal Perturbations of Laurent Matrices

Gebert, Martin und Rojas-Molina, Constanza (2022): Lifshitz Tails for Random Diagonal Perturbations of Laurent Matrices. In: Annales Henri Poincare, Bd. 23, Nr. 11: S. 4149-4170

Abstract

We study the integrated density of states of one-dimensional random operators acting on l(2) (Z) of the form T + V-omega where T is a Laurent (also called bi-infinite Toeplitz) matrix and V-omega is an Anderson potential generated by i.i.d. random variables. We assume that the operator T is associated with a bounded, Holder-continuous symbol f , that attains its minimum at a finite number of points. We allow for f to attain its minima algebraically. The resulting operator T is long-range with weak (algebraic) off-diagonal decay. We prove that this operator exhibits Lifshitz tails at the lower edge of the spectrum with an exponent given by the integrated density of states of T at the lower spectral edge. The proof relies on generalizations of Dirichlet-Neumann bracketing to the long-range setting and an adaption of Temple's inequality.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Informatik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 1424-0637
• Sprache: Englisch