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

Raimundas Vidunas; Akimichi Takemura

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arXiv · 1609.01799

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

Raimundas Vidunas·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 m=2,3) or conjectured.

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Raimundas Vidunas, Akimichi Takemura. 2016-09-07. Differential relations for the largest root distribution of complex non-central Wishart matrices. https://arxiv.org/abs/1609.01799

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