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

TL;DR

This paper derives the distribution of the largest eigenvalue in a quaternionic Wishart model with a rank 1 spike, revealing a phase transition and connecting it to the GOE Tracy–Widom distribution.

Contribution

It provides the first analysis of the largest eigenvalue distribution in the quaternionic spiked Wishart model, extending the Laguerre symplectic ensemble to the soft edge.

Findings

Identifies a phase transition in the eigenvalue distribution

At the phase change, the distribution converges to GOE Tracy–Widom

First statistical analysis of the quaternionic Wishart ensemble at the soft edge

Abstract

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.