Asymptotics of block Toeplitz determinants with piecewise continuous symbols

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2024-08-28 DOI:10.1002/cpa.22223

Estelle Basor, Torsten Ehrhardt, Jani A. Virtanen

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Abstract

We determine the asymptotics of the block Toeplitz determinants $det T_{n} (ϕ)$ as $n \to \infty$ for $N \times N$ matrix-valued piecewise continuous functions $ϕ$ with a finitely many jumps under mild additional conditions. In particular, we prove that

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具有片断连续符号的块托普利兹行列式的渐近论

在温和的附加条件下，我们确定了块托普利兹行列式的渐近线，如同具有有限次跳跃的矩阵值片断连续函数。特别是，我们证明了，，和是取决于矩阵符号的常数，并在我们的主要结果中进行了描述。我们的方法基于托普利兹行列式的新局部定理、计算具有片断连续矩阵值符号的托普利兹算子的弗雷德霍姆指数的新方法以及其他算子理论方法。作为我们结果的一个应用，我们考虑了在量子自旋链模型的纠缠熵研究中出现的片断连续符号。

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.