Universal Scaling Limits of the Symplectic Elliptic Ginibre Ensemble

IF 0.9 4区 数学 Q4 PHYSICS, MATHEMATICAL Random Matrices-Theory and Applications Pub Date : 2021-08-12 DOI:10.1142/S2010326322500472
Sunggyu Byun, M. Ebke
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引用次数: 15

Abstract

. We consider the eigenvalues of symplectic elliptic Ginibre matrices which are known to form a Pfaffian point process whose correlation kernel can be expressed in terms of the skew-orthogonal Hermite polynomials. We derive the scaling limits and the convergence rates of the correlation functions at the real bulk/edge of the spectrum, which in particular establishes the local universality at strong non-Hermiticity. Furthermore, we obtain the subleading corrections of the edge correlation kernels, which depend on the non-Hermiticity parameter contrary to the universal leading term. Our proofs are based on the asymptotic behaviour of the complex elliptic Ginibre ensemble due to Lee and Riser as well as on a version of the Christoffel-Darboux identity, a differential equation satisfied by the skew-orthogonal polynomial kernel.
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辛椭圆型Ginibre系综的普遍标度极限
. 我们考虑辛椭圆型Ginibre矩阵的特征值,已知它们构成一个Pfaffian点过程,其相关核可以用斜正交埃尔米特多项式表示。我们推导了相关函数在谱实块/谱边处的尺度极限和收敛速率,特别地建立了在强非厄米性处的局部普适性。此外,我们还得到了边缘相关核的子导校正,该子导校正依赖于与通用导项相反的非厄米参数。我们的证明是基于复椭圆Ginibre系综的渐近行为,由Lee和Riser以及一个版本的Christoffel-Darboux恒等式,一个由斜正交多项式核满足的微分方程。
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来源期刊
Random Matrices-Theory and Applications
Random Matrices-Theory and Applications Decision Sciences-Statistics, Probability and Uncertainty
CiteScore
1.90
自引率
11.10%
发文量
29
期刊介绍: Random Matrix Theory (RMT) has a long and rich history and has, especially in recent years, shown to have important applications in many diverse areas of mathematics, science, and engineering. The scope of RMT and its applications include the areas of classical analysis, probability theory, statistical analysis of big data, as well as connections to graph theory, number theory, representation theory, and many areas of mathematical physics. Applications of Random Matrix Theory continue to present themselves and new applications are welcome in this journal. Some examples are orthogonal polynomial theory, free probability, integrable systems, growth models, wireless communications, signal processing, numerical computing, complex networks, economics, statistical mechanics, and quantum theory. Special issues devoted to single topic of current interest will also be considered and published in this journal.
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