Lindner, Marko : A note on the spectrum of bi-infinite bi-diagonal random matrices

Author(s):

Lindner, Marko

Title:

A note on the spectrum of bi-infinite bi-diagonal random matrices

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 12, 2008

Mathematics Subject Classification:

47B80			[ Random operators ]
47A10			[ Spectrum, resolvent ]
47B36			[ Jacobi and generalizations ]

Abstract:

The purpose of this note is to demonstrate the use of the results from the two recent papers [5] and [6] by Chandler-Wilde and the author for the explicit computation of the spectrum of two-sided infinite matrices with random diagonals. Here we consider the case of two random diagonals, one of them the main diagonal. Our result is a generalization of Theorem 8.1 in [24] by Trefethen, Contedini and Embree from the case of one random and one constant diagonal to the case of two random diagonals.

Keywords:

random matrix, spectral theory, Jacobi matrix, operators on $\ell^p$

Language:

English

Publication time:

5 / 2008