Calculation and properties of zonal polynomials

DOI10.1007/s11786-020-00458-0zbMath1462.05350arXiv2001.11599OpenAlexW3103297828MaRDI QIDQ2209263

Christoph Koutschan, Lin Jiu

Publication date: 30 October 2020

Published in: Mathematics in Computer Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.11599

zbMATH Keywords

symmetric functionLaplace-Beltrami operatorWishart matrixinteger partitionzonal polynomialhypergeometric function of a matrix argument

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Symmetric functions and generalizations (05E05) Other hypergeometric functions and integrals in several variables (33C70) Random matrices (algebraic aspects) (15B52) Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (3)

PROPERTIES OF THE INVERSE OF A NONCENTRAL WISHART MATRIX ⋮ Algorithm for the product of Jack polynomials and its application to the sphericity test ⋮ Numerical computation for the exact distribution of Roy's largest root statistic under linear alternative

Uses Software

• Mathematica
• SageMath
• DLMF
• HolonomicFunctions
• SF
• hgm R

Cites Work

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• The efficient evaluation of the hypergeometric function of a matrix argument
• The holonomic gradient method for the distribution function of the largest root of a Wishart matrix
• Exact distributional computations for Roy's statistic and the largest eigenvalue of a Wishart distribution
• Holonomic gradient descent and its application to the Fisher-Bingham integral
• Formulas for zonal polynomials
• On the distribution of the largest eigenvalue in principal components analysis
• A Maple package for symmetric functions
• System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions
• Special Functions of Matrix Argument. I: Algebraic Induction, Zonal Polynomials, and Hypergeometric Functions
• A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
• Calculation of Zonal Polynomial Coefficients by Use of the Laplace-Beltrami Operator
• Systems of Partial Differential Equations for Hypergeometric Functions of Matrix Argument

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