Results 21 to 25 of about 147 (25)

Anderson localization for CMV matrices with Verblunsky coefficients defined by the hyperbolic toral automorphism [PDF]

arXiv
In this paper, we prove the large deviation estimates and Anderson localization for CMV matrices on $\ell^2(\mathbb{Z}_+)$ with Verblunsky coefficients defined dynamically by the hyperbolic toral automorphism. Part of positivity results on the Lyapunov exponents of Chulaevsky-Spencer and Anderson localization results of Bourgain-Schlag on Schr\"{o ...
arxiv  

Interval spectrum for electric quantum walk and related skew-shift CMV matrices [PDF]

arXiv
We show that for a family of quantum walk models with electric fields, the spectrum is the unit circle for any irrational field. The result also holds for the associated CMV matrices defined by skew-shifts. Generalizations to CMV matrices with skew-shifts on higher dimensional torus are also obtained.
arxiv  

Finite and full scale localization for the multi-frequency quasi-periodic CMV matrices [PDF]

arXiv
This paper formulates the finite and full-scale localization for multi-frequency quasi-periodic CMV matrices. This can be viewed as the CMV counterpart to the localization results by Goldstein, Schlag, and Voda [arXiv:1610.00380 (math.SP], Invent. Math. 217 (2019)) on multi-frequency quasi-periodic Schr\"{o}dinger operators.
arxiv  

The CMV bispectrality of the Jacobi polynomials on the unit circle [PDF]

arXiv
We show that the Jacobi polynomials that are orthogonal on the unit circle (the Jacobi OPUC) are CMV bispectral. This means that the corresponding Laurent polynomials in the CMV basis satisfy two dual ordinary eigenvalue problems: a recurrence relation and a differential equation of Dunkl type.
arxiv  

Exploring Commercial Vehicle Detouring Patterns through the Application of Probe Trajectory Data [PDF]

arXiv
Understanding motorist detouring behavior is critical for both traffic operations and planning applications. However, measuring real-world detouring behavior is challenging due to the need to track the movement of individual vehicles. Recent developments in high-resolution vehicle trajectory data have enabled transportation professionals to observe ...
arxiv