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

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