English

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 β\beta Ensembles and their spectral properties are analyzed.

Keywords

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

R2 v1 2026-06-21T09:04:57.214Z