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.
"The largest sample eigenvalue distribution in the rank 1 quaternionic spiked model of Wishart ensemble." Ann. Probab. 37 (4) 1273 - 1328, July 2009. https://doi.org/10.1214/08-AOP432