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

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

2007-11-19

arxiv.org/abs/0711.2722v2

Annals of Probability 2009, Vol. 37, No. 4, 1273-1328

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AOP432 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/08-AOP432

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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