Advanced Studies in Pure Mathematics

Differential relations for the largest root distribution of complex non-central Wishart matrices

Raimundas Vidunas and Akimichi Takemura

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Abstract

A holonomic system for the probability density function of the largest eigenvalue of a non-central complex Wishart distribution with identity covariance matrix is derived. Furthermore a new determinantal formula for the probability density function is derived (for the dimensions $m=2,3$) or conjectured.

Article information

Source
The 50th Anniversary of Gröbner Bases, T. Hibi, ed. (Tokyo: Mathematical Society of Japan, 2018), 411-436

Dates
Received: 31 August 2016
First available in Project Euclid: 21 September 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1537499608

Digital Object Identifier
doi:10.2969/aspm/07710411

Mathematical Reviews number (MathSciNet)
MR3839716

Zentralblatt MATH identifier
07034259

Subjects
Primary: 60E05: Distributions: general theory 13N10: Rings of differential operators and their modules [See also 16S32, 32C38] 62H10: Distribution of statistics

Keywords
complex Wishart distribution holonomic systems

Citation

Vidunas, Raimundas; Takemura, Akimichi. Differential relations for the largest root distribution of complex non-central Wishart matrices. The 50th Anniversary of Gröbner Bases, 411--436, Mathematical Society of Japan, Tokyo, Japan, 2018. doi:10.2969/aspm/07710411. https://projecteuclid.org/euclid.aspm/1537499608


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