## Advanced Studies in Pure Mathematics

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

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

Raimundas Vidunas and Akimichi Takemura

#### 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