The Annals of Probability

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

Dong Wang

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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.

Article information

Source
Ann. Probab., Volume 37, Number 4 (2009), 1273-1328.

Dates
First available in Project Euclid: 21 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.aop/1248182139

Digital Object Identifier
doi:10.1214/08-AOP432

Mathematical Reviews number (MathSciNet)
MR2546746

Zentralblatt MATH identifier
1176.15047

Subjects
Primary: 15A52 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]
Secondary: 60F99: None of the above, but in this section

Keywords
Wishart distribution quaternionic spiked model

Citation

Wang, Dong. The largest sample eigenvalue distribution in the rank 1 quaternionic spiked model of Wishart ensemble. Ann. Probab. 37 (2009), no. 4, 1273--1328. doi:10.1214/08-AOP432. https://projecteuclid.org/euclid.aop/1248182139


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