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.
@article{1248182139,
author = {Wang, Dong},
title = {The largest sample eigenvalue distribution in the rank 1 quaternionic spiked model of Wishart ensemble},
journal = {Ann. Probab.},
volume = {37},
number = {1},
year = {2009},
pages = { 1273-1328},
language = {en},
url = {http://dml.mathdoc.fr/item/1248182139}
}
Wang, Dong. The largest sample eigenvalue distribution in the rank 1 quaternionic spiked model of Wishart ensemble. Ann. Probab., Tome 37 (2009) no. 1, pp. 1273-1328. http://gdmltest.u-ga.fr/item/1248182139/