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