The largest sample eigenvalue distribution in the rank 1 quaternionic spiked model of Wishart ensemble

2007/11/30 by Dong Wang · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Geometry #Bayesian Methods and Mixture Models #Random Matrices and Applications #math.PR #msc:15A52 #msc:41A60 #msc:60F99

paper · pdf · doi:10.1214/08-aop432

published as Annals of Probability 2009, Vol. 37, No. 4, 1273-1328 · Published in at http://dx.doi.org/10.1214/08-AOP432 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2009/07/01 · arxiv created 2009/10/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We solve the largest sample eigenvalue distribution problem in the rank 1 spiked model of the quaternionic Wishart ensemble, which is the first case of a statistical generalization of the Laguerre symplectic ensemble (LSE) on the soft edge. We observe a phase change phenomenon similar to that in the complex case, and prove that the new distribution at the phase change point is the GOE Tracy–Widom distribution.

Citations

• On the distribution of the largest eigenvalue in principal components analysis
• Painlevé transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles
• Correlation Functions, Cluster Functions, and Spacing Distributions for Random Matrices
• Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges

Cited by

• Universality in Complex Wishart ensembles: The 2 cut case

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