{"title":"Scaling limits of complex and symplectic non-Hermitian Wishart ensembles","authors":"Sung-Soo Byun , Kohei Noda","doi":"10.1016/j.jat.2025.106148","DOIUrl":null,"url":null,"abstract":"<div><div>Non-Hermitian Wishart matrices were introduced in the context of quantum chromodynamics with a baryon chemical potential. These provide chiral extensions of the elliptic Ginibre ensembles as well as non-Hermitian extensions of the classical Wishart/Laguerre ensembles. In this work, we investigate eigenvalues of non-Hermitian Wishart matrices in the symmetry classes of complex and symplectic Ginibre ensembles. We introduce a generalised Christoffel–Darboux formula in the form of a certain second-order differential equation, offering a unified and robust method for analysing correlation functions across all scaling regimes in the model. By employing this method, we derive bulk and edge scaling limits for eigenvalue correlations at both strong and weak non-Hermiticity.</div></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"308 ","pages":"Article 106148"},"PeriodicalIF":0.6000,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Approximation Theory","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021904525000061","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Non-Hermitian Wishart matrices were introduced in the context of quantum chromodynamics with a baryon chemical potential. These provide chiral extensions of the elliptic Ginibre ensembles as well as non-Hermitian extensions of the classical Wishart/Laguerre ensembles. In this work, we investigate eigenvalues of non-Hermitian Wishart matrices in the symmetry classes of complex and symplectic Ginibre ensembles. We introduce a generalised Christoffel–Darboux formula in the form of a certain second-order differential equation, offering a unified and robust method for analysing correlation functions across all scaling regimes in the model. By employing this method, we derive bulk and edge scaling limits for eigenvalue correlations at both strong and weak non-Hermiticity.
期刊介绍：
The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others:
• Classical approximation
• Abstract approximation
• Constructive approximation
• Degree of approximation
• Fourier expansions
• Interpolation of operators
• General orthogonal systems
• Interpolation and quadratures
• Multivariate approximation
• Orthogonal polynomials
• Padé approximation
• Rational approximation
• Spline functions of one and several variables
• Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds
• Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth)
• Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis
• Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth)
• Gabor (Weyl-Heisenberg) expansions and sampling theory.
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