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Related papers: On lacunary Toeplitz determinants

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This work provides the general framework for obtaining strong Szeg\H{o} limit theorems for multi-bordered, semi-framed, framed, and multi-framed Toeplitz determinants, extending the results of Basor et al. (2022) beyond the (single)…

Classical Analysis and ODEs · Mathematics 2024-07-16 Roozbeh Gharakhloo

In this paper, we develop the Riemann-Hilbert method to study the asymptotics of discrete orthogonal polynomials on infinite nodes with an accumulation point. To illustrate our method, we consider the Tricomi-Carlitz polynomials…

Classical Analysis and ODEs · Mathematics 2014-10-16 Xiao-Bo Wu , Yu Lin , Shuai-Xia Xu , Yu-Qiu Zhao

In this paper, we are interested in matrix valued orthogonal polynomials on the real line with respect to exponential weights. We obtain strong asymptotics as the degree tends to infinity in different regions of the complex plane, as well…

Classical Analysis and ODEs · Mathematics 2026-04-21 Alfredo Deaño , Pablo Román

In the past few years we have derived asymptotic expansions for lambda_d of the dimer problem and lambda_d(p) of the monomer-dimer problem. The many expansions so far computed are collected herein. We shine a light on results in two…

Mathematical Physics · Physics 2013-02-18 Paul Federbush

We propose an asymptotic expansion formula for matrix integrals, including oscillatory terms (derivatives of theta-functions) to all orders. This formula is heuristically derived from the analogy between matrix integrals, and formal matrix…

Mathematical Physics · Physics 2009-03-27 Bertrand Eynard

We consider the eigenvalues of the Dirichlet and Neumann Laplacians on a bounded domain with Lipschitz boundary and prove two-term asymptotics for their Riesz means of arbitrary positive order. Moreover, when the underlying domain is…

Spectral Theory · Mathematics 2025-08-11 Rupert L. Frank , Simon Larson

In this paper, we study the full asymptotic expansion of the partition functions of determinantal point processes defined on a polarized K\"ahler manifold. We show that the coefficients of the expansion are given by geometric functionals on…

Differential Geometry · Mathematics 2026-01-01 Kiyoon Eum

We investigate a Riemann-Hilbert problem (RHP), whose solution corresponds to a group of $q$-orthogonal polynomials studied earlier by Ismail et al. Using RHP theory we determine new asymptotic results in the limit as the degree of the…

Classical Analysis and ODEs · Mathematics 2023-08-01 Nalini Joshi , Tomas Lasic Latimer

We establish an asymptotic formula for determinants of truncated Wiener-Hopf+Hankel operators with symbol equal to the exponential of a constant times the characteristic function of an interval. This is done by reducing it to the…

Functional Analysis · Mathematics 2007-05-23 Estelle L. Basor , Torsten Ehrhardt , Harold Widom

We prove asymptotic formulas for Toeplitz determinants generated by functions with sequences of Fourier coefficients belonging to weighted Orlicz sequence classes. We concentrate our attention on the case of nonvanishing generating…

Functional Analysis · Mathematics 2007-05-23 Alexei Yu. Karlovich

We study averages of multiplicative eigenvalue statistics in ensembles of orthogonal Haar distributed matrices, which can alternatively be written as Toeplitz+Hankel determinants. We obtain new asymptotics for symbols with Fisher-Hartwig…

Mathematical Physics · Physics 2020-08-19 Tom Claeys , Gabriel Glesner , Alexander Minakov , Meng Yang

We consider the large-$N$ asymptotics of a system of discrete orthogonal polynomials on an infinite regular lattice of mesh $\frac{1}{N}$, with weight $e^{-NV(x)}$, where $V(x)$ is a real analytic function with sufficient growth at…

Mathematical Physics · Physics 2010-07-07 Pavel Bleher , Karl Liechty

We consider canonical determinantal random point processes with N particles on a compact Riemann surface X defined with respect to the constant curvature metric. In the higher genus (hyperbolic) cases these point processes may be defined in…

Mathematical Physics · Physics 2011-08-18 Robert J. Berman

This paper aims to study the asymptotic expansion of analytic torsion forms associated with a certain series of flat bundles. We prove the existence of the full expansion and give a formula for the sub-leading term, while Bismut-Ma-Zhang…

Differential Geometry · Mathematics 2023-01-11 Qiaochu Ma

In this paper, we derive new asymptotic expansions for the solutions of higher order elliptic equations in the presence of small inclusions. As a byproduct, we derive a topological derivative based algorithm for the reconstruction of…

Analysis of PDEs · Mathematics 2020-01-01 Andrea Aspri , Elena Beretta , Otmar Scherzer , Monika Muszkieta

The paper is devoted to exact and asymptotic formulas for the determinants of Toeplitz matrices with perturbations by blocks of fixed size in the four corners. If the norms of the inverses of the unperturbed matrices remain bounded as the…

Functional Analysis · Mathematics 2014-07-22 Albrecht Boettcher , Lenny Fukshansky , Stephan Ramon Garcia , Hiren Maharaj

We study the regularized determinants ${\rm det}\, \Delta$ of various self-adjoint extensions of symmetric Laplacians acting in spinor bundles over compact Riemann surfaces with flat singular metrics $|\omega|^2$, where $\omega$ is a…

Differential Geometry · Mathematics 2025-11-25 Alexey Kokotov , Dmitrii Korikov

In the paper, we consider the extended Gross-Witten-Wadia unitary matrix model by introducing a logarithmic term in the potential. The partition function of the model can be expressed equivalently in terms of the Toeplitz determinant with…

Mathematical Physics · Physics 2024-02-20 Yu Chen , Shuai-Xia Xu , Yu-Qiu Zhao

We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal…

Mathematical Physics · Physics 2007-05-23 N. M. Ercolani , K. D. T-R McLaughlin

In this paper, we compute the small and large $x$ asymptotics of the special function solutions of Painlev\'e-III equation in the complex plane. We use the representation in terms of Toeplitz determinants of Bessel functions obtained in…

Classical Analysis and ODEs · Mathematics 2025-05-06 Hao Pan , Andrei Prokhorov