Differential relations for the largest root distribution of complex non-central Wishart matrices
Raimundas Vidunas, Akimichi Takemura
TL;DR
This paper derives a holonomic system and a new determinantal formula for the probability density function of the largest eigenvalue of non-central complex Wishart matrices, advancing understanding of their spectral distribution.
Contribution
It introduces a holonomic system and a conjectured determinantal formula for the largest eigenvalue distribution of non-central complex Wishart matrices.
Findings
Holonomic system for the eigenvalue distribution derived.
New determinantal formula proposed for specific matrix sizes.
Conjecture extends the formula to larger 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 m=2,3) or conjectured.
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Taxonomy
TopicsRandom Matrices and Applications · Morphological variations and asymmetry · Advanced Statistical Methods and Models