Rostyslav Kozhan

activity

20092026

most citedMatrix models and eigenvalue statistics for truncations of classical ensembles of random unitary matrices

12 citations · 38 across the 23 of their papers we have counts for

collaborators

26 papers

math.CV2026

Zeros of Laurent multiple orthogonal polynomials on the unit circle

Rostyslav Kozhan, Marcus Vaktnäs

We investigate two distinct formulations of Laurent multiple orthogonal polynomials on the unit circle, introduced in arXiv:2410.12094 and arXiv:2601.04783 respectively. For the fi…

math.CA2026

Szegő Mapping and Hermite--Padé Polynomials for Multiple Orthogonality on the Unit Circle

Rostyslav Kozhan, Marcus Vaktnäs

We investigate generalized Laurent multiple orthogonal polynomials on the unit circle satisfying simultaneous orthogonality conditions with respect to $r$ probability measures or l…

math.CA2025

Ratio asymptotics and zero density for orthogonal polynomials with varying Verblunsky coefficients

Rostyslav Kozhan, František Štampach

We study asymptotic behavior of orthogonal polynomials on the unit circle with varying Verblunsky coefficients $α_{n, N}$ when the ratio $n / N$ converges as $n, N \to \infty$ . First, we…

math.CA2025

Zeros of Multiple Orthogonal Polynomials: Location and Interlacing

Rostyslav Kozhan, Marcus Vaktnäs

We prove a criterion on the possible locations of zeros of type I and type II multiple orthogonal polynomials in terms of normality of degree $1$ Christoffel transforms. We provide…

math.CA2024★ 1 cited

Nikishin systems on the unit circle

Rostyslav Kozhan

We introduce Nikishin system of $r$ probability measures on the unit circle. We show that such systems satisfy the AT property and therefore normality, introduced in~\cite{KVMLOPUC…

math.CA2024★ 1 cited

Angelesco and AT systems on the Unit Circle

Rostyslav Kozhan, Marcus Vaktnäs

We introduce the concept of Laurent multiple orthogonality on the unit circle and define Angelesco and AT systems in this setting. Using a generalized Andreief identity, we establi…

math.CA2024

Determinantal Formulas for Rational Perturbations of Multiple Orthogonality Measures

Rostyslav Kozhan, Marcus Vaktnäs

Given multiple orthogonal polynomials on the real line with respect to a system $μ = (μ_{1}, \dots, μ_{r})$ , we investigate multiple orthogonal polynomials associated with any ration…

math.CA2024★ 1 cited

Christoffel Transform and Multiple Orthogonal Polynomials

Rostyslav Kozhan, Marcus Vaktnäs

We investigate multiple orthogonal polynomials associated with the system of measures obtained by applying a Christoffel transform to each of the orthogonality measures. We present…

math.CA2024

Szegő Recurrence for Multiple Orthogonal Polynomials on the Unit Circle

Marcus Vaktnäs, Rostyslav Kozhan

We investigate polynomials that satisfy simultaneous orthogonality conditions with respect to several measures on the unit circle. We generalize the direct and inverse Szegő recurr…

math.PR2023

Multiplicative non-Hermitian perturbations of classical $β$ -ensembles

Gökalp Alpan, Rostyslav Kozhan

We compute the joint eigenvalue distribution for a multiplicative non-Hermitian perturbation $(I + i Γ) H$ , $rank Γ = 1$ of a random matrix $H$ from the Gaussian, Laguerr…

math.CA2023

A generalized Hermite-Biehler theorem

Rostyslav Kozhan, Mikhail Tyaglov

The classical Hermite-Biehler theorem describes possible zero sets of complex linear combinations of two real polynomials whose zeros strictly interlace. We provide the full charac…

math.PR2021

Hermitian and non-Hermitian perturbations of chiral Gaussian $β$ -ensembles

Gökalp Alpan, Rostyslav Kozhan

We compute the joint eigenvalue distribution for the rank one Hermitian and non-Hermitian perturbations of chiral Gaussian $β$ -ensembles ( $β > 0$ ) of random matrices.

math.PR2019

Global fluctuations for Multiple Orthogonal Polynomial Ensembles

Maurice Duits, Benjamin Fahs, Rostyslav Kozhan

We study the fluctuations of linear statistics with polynomial test functions for Multiple Orthogonal Polynomial Ensembles. Multiple Orthogonal Polynomial Ensembles form an importa…

math.CA2019

Differential equations for the recurrence coefficients limits for multiple orthogonal polynomials from a Nevai class

Alexander I. Aptekarev, Rostyslav Kozhan

A limiting property of the nearest-neighbor recurrence coefficients for multiple orthogonal polynomials from a Nevai class is investigated. Namely, assuming that the nearest-neighb…

math-ph2018

On Gaussian random matrices coupled to the discrete Laplacian

Rostyslav Kozhan

We study operators obtained by coupling an $n \times n$ random matrix from one of the Gaussian ensembles to the discrete Laplacian. We find the joint distribution of the eigenvalue…

math-ph2016

Relative Szegő asymptotics for Toeplitz determinants

Maurice Duits, Rostyslav Kozhan

We study the asymptotic behavior, as $n \to \infty$ , of ratios of Toeplitz determinants $D_{n} (e^{h} d μ) / D_{n} (d μ)$ defined by a measure $μ$ on the unit circle and a sufficiently smooth fu…

math.PR2015

Rank one non-Hermitian perturbations of Hermitian $β$ -ensembles

Rostyslav Kozhan

For any $β > 0$ , we provide a tridiagonal matrix model and compute the joint eigenvalue density of a random rank one non-Hermitian perturbation of Gaussian and Laguerre $β$ -ensembles…

math.PR2015★ 12 cited

Matrix models and eigenvalue statistics for truncations of classical ensembles of random unitary matrices

Rowan Killip, Rostyslav Kozhan

We consider random non-normal matrices constructed by removing one row and column from samples from Dyson's circular ensembles or samples from the classical compact groups. We deve…

math-ph2014★ 7 cited

Finite range perturbations of finite gap Jacobi and CMV operators

Rostyslav Kozhan

Necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range perturbation of a Jacobi or CMV operator from a finite gap isospectral…

math.CA2012★ 2 cited

Spectral and resonance problem for perturbations of periodic Jacobi operators

Rostyslav Kozhan

Necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range or exponentially decaying perturbation of a periodic Jacobi operator. A…

math.SP2012★ 6 cited

Asymptotics of the Eigenvalues of Two-Diagonal Jacobi Matrices

Rostyslav Kozhan

We compute the asymptotics of eigenvalues of Jacobi matrices with the zero coefficients on the main diagonal and the off-diagonal coefficients which converge to zero.

math.CA2012★ 2 cited

L1-spectrum of Banach space valued Ornstein-Uhlenbeck operators

Rostyslav Kozhan

We characterize the $L^{1} (E; μ_{\infty})$ -spectrum of the Ornstein-Uhlenbeck operator, where $μ_{\infty}$ is the invariant measure for the Ornstein-Uhlenbeck semigroup. The main result c…

math.SP2012★ 1 cited

Meromorphic continuations of finite gap Herglotz functions and periodic Jacobi matrices

Rostyslav Kozhan

We find a necessary and sufficient condition for a Herglotz function $m$ to be the Borel transform of the spectral measure of an exponentially decaying perturbation of a periodic J…

math.AP2011

Jost asymptotics for matrix orthogonal polynomials on the real line

Rostyslav Kozhan

We obtain matrix-valued Jost asymptotics for block Jacobi matrices under an L1-type condition on Jacobi parameters, and give a necessary and sufficient condition for an analytic ma…

Zeros of Laurent multiple orthogonal polynomials on the unit circle

Szegő Mapping and Hermite--Padé Polynomials for Multiple Orthogonality on the Unit Circle

Ratio asymptotics and zero density for orthogonal polynomials with varying Verblunsky coefficients

Zeros of Multiple Orthogonal Polynomials: Location and Interlacing

Nikishin systems on the unit circle

Angelesco and AT systems on the Unit Circle

Determinantal Formulas for Rational Perturbations of Multiple Orthogonality Measures

Christoffel Transform and Multiple Orthogonal Polynomials

Szegő Recurrence for Multiple Orthogonal Polynomials on the Unit Circle

Multiplicative non-Hermitian perturbations of classical β-ensembles

A generalized Hermite-Biehler theorem

Hermitian and non-Hermitian perturbations of chiral Gaussian β-ensembles

Global fluctuations for Multiple Orthogonal Polynomial Ensembles

Differential equations for the recurrence coefficients limits for multiple orthogonal polynomials from a Nevai class

On Gaussian random matrices coupled to the discrete Laplacian

Relative Szegő asymptotics for Toeplitz determinants

Rank one non-Hermitian perturbations of Hermitian β-ensembles

Matrix models and eigenvalue statistics for truncations of classical ensembles of random unitary matrices

Finite range perturbations of finite gap Jacobi and CMV operators

Spectral and resonance problem for perturbations of periodic Jacobi operators

Asymptotics of the Eigenvalues of Two-Diagonal Jacobi Matrices

L1-spectrum of Banach space valued Ornstein-Uhlenbeck operators

Meromorphic continuations of finite gap Herglotz functions and periodic Jacobi matrices

Jost asymptotics for matrix orthogonal polynomials on the real line

Multiplicative non-Hermitian perturbations of classical $β$ -ensembles

Hermitian and non-Hermitian perturbations of chiral Gaussian $β$ -ensembles

Rank one non-Hermitian perturbations of Hermitian $β$ -ensembles