Related papers: Right limits and reflectionless measures for CMV m…
This paper studies the inverse Steklov spectral problem for curvilinear polygons. For generic curvilinear polygons with angles less than $\pi$, we prove that the asymptotics of Steklov eigenvalues obtained in arXiv:1908.06455 determines, in…
We continue studying polynomials generated by the Szeg\H{o} recursion when a finite number of Verblunsky coefficients lie outside the closed unit disk. We prove some asymptotic results for the corresponding orthogonal polynomials and then…
We develop a modern extended scattering theory for CMV matrices with asymptotically constant Verblunsky coefficients. We demonstrate that an orthonormal system in a certain "weighted'' Hilbert space, which we call the Fadeev-Marchenko (FM)…
We provide a very general result that identifies the essential spectrum of broad classes of operators as exactly equal to the closure of the union of the spectra of suitable limits at infinity. Included is a new result on the essential…
We introduce and study a special family of polynomials orthogonal on the unit circle (OPUC). These OPUC satisfy a mirror symmetry property of their Verblunsky coefficients. Several equivalent conditions for the OPUC to be mirror symmetric…
We prove that dynamically defined Jacobi and CMV matrices associated with generic continuous sampling functions have all gaps predicted by the Gap Labelling Theorem open. We also give a mechanism for generic gap opening for quasi-periodic…
M. Derevyagin, L. Vinet and A. Zhedanov introduced in Constr. Approx. 36 (2012) 513-535 a new connection between orthogonal polynomials on the unit circle and the real line. It maps any real CMV matrix into a Jacobi one depending on a real…
We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps $T_\alpha$ using the full parameter range $0<…
This paper deals with general structural properties of one-dimensional Schr"odinger operators with some absolutely continuous spectrum. The basic result says that the omega limit points of the potential under the shift map are…
In this paper, we propose optimal tests for circular reflective symmetry about a fixed median direction. The distributions against which optimality is achieved are the so-called k-sine-skewed distributions of Umbach and Jammalamadaka…
While subspace identification methods (SIMs) are appealing due to their simple parameterization for MIMO systems and robust numerical realizations, a comprehensive statistical analysis of SIMs remains an open problem, especially in the…
There is a vast theory of the asymptotic behavior of orthogonal polynomials with respect to a measure on $\mathbb{R}$ and its applications to Jacobi matrices. That theory has an obvious affine invariance and a very special role for…
A simple example is used to show that renormalization group limit cycles of effective quantum theories can be studied in a new way. The method is based on the similarity renormalization group procedure for Hamiltonians. The example contains…
We study several related aspects of reflectionless Jacobi matrices. Our first set of results deals with the singular part of reflectionless measures. We then introduce and discuss Lyapunov exponents, density of states measures, and other…
In this paper, we study a class of multilinear Gibbs measures with Hamiltonian given by a generalized $\mathrm{U}$-statistic and with a general base measure. Expressing the asymptotic free energy as an optimization problem over a space of…
In a previous paper we study the neutrino-electron scattering in the framework of a left-right symmetric model (LRSM). Constraints on the LRSM parameters $M_{Z_{2}}$ and $\phi$ were obtained. Based on new measurements we present an update…
The reduced density matrices (RDMs) are calculated in the thermodynamic limit for the Chern-Simons non-relativistic particle system and Maxwell-Boltzmann (MB) statistics. It is established that they are zero outside of a diagonal and…
Several well-known results from the random matrix theory, such as Wigner's law and the Marchenko--Pastur law, can be interpreted (and proved) in terms of non-backtracking walks on a certain graph. Orthogonal polynomials with respect to the…
We consider non-Hermitian random matrices $X \in \mathbb{C}^{n \times n}$ with general decaying correlations between their entries. For large $n$, the empirical spectral distribution is well approximated by a deterministic density,…
We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the martingale, we prove that normalized moments of…