## Advanced Studies in Pure Mathematics

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

#### 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

Dates
First available in Project Euclid: 21 September 2018

https://projecteuclid.org/ euclid.aspm/1537499608

Digital Object Identifier
doi:10.2969/aspm/07710411

Mathematical Reviews number (MathSciNet)
MR3839716

Zentralblatt MATH identifier
07034259

#### 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