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arXiv · 0711.2722

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.

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Dong Wang. 2009-10-12. The largest sample eigenvalue distribution in the rank 1 quaternionic spiked model of Wishart ensemble. https://doi.org/10.1214/08-aop432

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