Anderson localization for Jacobi matrices associated with high-dimensional skew shifts

TL;DR

This paper proves Anderson localization for a class of Jacobi matrices linked to high-dimensional skew shifts, expanding understanding of localization phenomena in complex dynamical systems.

Contribution

It establishes Anderson localization for Jacobi matrices associated with skew shifts on high-dimensional tori, a novel extension to previous lower-dimensional results.

Findings

Proves Anderson localization for high-dimensional skew shift systems.

Extends localization results to a new class of Jacobi matrices.

Provides mathematical framework for analyzing localization in complex dynamical settings.

Abstract

In this paper, we establish Anderson localization for a class of Jacobi matrices associated with skew shifts on $\mathbb{T}^{d}$, $d\geq3$.