Matrix Product Ensembles of Hermite Type and the Hyperbolic Harish-Chandra-Itzykson-Zuber Integral

Forrester P. J.; Ipsen J. R.; Liu Dang-Zheng

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Matrix Product Ensembles of Hermite Type and the Hyperbolic Harish-Chandra-Itzykson-Zuber Integral

机译：Hermite类型和双曲线哈里什 - Chandra-Itzykson-Zuber积分矩阵产品集合

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We investigate spectral properties of a Hermitised random matrix product which, contrary to previous product ensembles, allows for eigenvalues on the full real line. We prove that the eigenvalues form a bi-orthogonal ensemble, which reduces asymptotically to the Hermite Muttalib-Borodin ensemble. Explicit expressions for the bi-orthogonal functions as well as the correlation kernel are provided. Scaling the latter near the origin gives a limiting kernel involving Meijer G-functions, and the functional form of the global density is calculated. As a part of this study, we introduce a new matrix transformation which maps the space of polynomial ensembles onto itself. This matrix transformation is closely related to the so-called hyperbolic Harish-Chandra-Itzykson-Zuber integral.

机译：我们调查了与以前的产品合奏相反的HermityAtheRatum Matrix产品的光谱特性，允许全部实际线上的特征值。我们证明了特征值形成了双正交合奏，这减少了对Hermite Muttalib-Borodin合奏的渐近。提供双正交功能的显式表达式以及相关内核。缩放后者附近的原点给出了一个限制涉及Meijer G函数的内核，并计算全局密度的功能形式。作为本研究的一部分，我们介绍了一种新的矩阵变换，将多项式集合的空间映射到自身上。该矩阵转换与所谓的双曲线Harish-Chandra-Itzykson-Zuber积分密切相关。

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《Annales Henri Poincare》 |2018年第5期|共42页
作者
Forrester P. J.; Ipsen J. R.; Liu Dang-Zheng;
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作者单位

Univ Melbourne Sch Math &

Stat ARC Ctr Excellence Math &

Stat Frontiers Parkville Vic 3010 Australia;

Univ Melbourne Sch Math &

Stat ARC Ctr Excellence Math &

Stat Frontiers Parkville Vic 3010 Australia;

Univ Sci &

Technol China Sch Math Sci Key Lab Wu Wen Tsun Math CAS Hefei 230026 Anhui Peoples R China;

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中图分类理论物理学;
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1. Matrix Product Ensembles of Hermite Type and the Hyperbolic Harish-Chandra-Itzykson-Zuber Integral [J] . Forrester P. J., Ipsen J. R., Liu Dang-Zheng Annales Henri Poincare . 2018,第5期

机译：Hermite类型和双曲线哈里什 - Chandra-Itzykson-Zuber积分矩阵产品集合
2. Hermite-Hadamard Type Inequalities for Products of Two Co-ordinated Convex Mappings via Fractional integrals [J] . Huseyin Budak, Mehmet Zeki Sarikaya International Journal of Applied Mathematics & Statistics . 2019,第4期

机译：Hermite-Hadamard通过分数积分的两个协调凸映射产品的不等式
3. Orthogonal and symplectic Harish-Chandra integrals and matrix product ensembles [J] . Forrester Peter J., Ipsen Jesper R., Liu Dang-Zheng, Random Matrices: Theory and Application . 2019,第4期

机译：正交和辛的Harish-Chandra积分和矩阵产品集成
4. Some New Hermite-Hadamard Type Inequalities for Quasi-Convex Functions via Fractional Integral Operator [C] . Erhan Set, Bari? ?elik, Ahmet Ocak Akdemir International Conference on Advances in Natural and Applied Sciences . 2017

机译：一些新的Hermite-Hadamard型以分数积分运算符对准凸函数的不等式
5. Identities, inequalities, Parseval type relations for integral transforms and fractional integrals [D] . Yurekli, Osman 1988

机译：积分变换和分数积分的恒等式，不等式，Parseval类型关系
6. Hermite–Hadamard type inequalities for F-convex function involving fractional integrals [O] . Pshtiwan Othman Mohammed, Mehmet Zeki Sarikaya -1

机译：涉及分数积分的F-凸函数的Hermite-Hadamard型不等式
7. Matrix product ensembles of Hermite-type [O] . Forrester, P. J., Ipsen, J. R., Liu, Dang-Zheng 2017

机译：Hermite型的矩阵产品集合

Matrix Product Ensembles of Hermite Type and the Hyperbolic Harish-Chandra-Itzykson-Zuber Integral

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