Spectral and Dynamical Properties of Certain Random Jacobi Matrices with Growing Parameters
Spectral Theory
2008-06-16 v2 Mathematical Physics
math.MP
Abstract
In this paper, a family of random Jacobi matrices, with off-diagonal terms that exhibit power-law growth, is studied. Since the growth of the randomness is slower than that of these terms, it is possible to use methods applied in the study of Schr\"odinger operators with random decaying potentials. A particular result of the analysis is the existence of operators with arbitrarily fast transport whose spectral measure is zero dimensional. The results are applied to the infinite Gaussian Ensembles and their spectral properties are analyzed.
Cite
@article{arxiv.0708.0670,
title = {Spectral and Dynamical Properties of Certain Random Jacobi Matrices with Growing Parameters},
author = {Jonathan Breuer},
journal= {arXiv preprint arXiv:0708.0670},
year = {2008}
}
Comments
26 pages, some typos corrected and some remarks added