Our paper “Extreme eigenvalue distributions of Jacobi ensembles: New exact representations, asymptotics and finite size corrections”, with Laureano Moreno-Pozas and Matthew McKay (HKUST) just appeared in Nuclear Physics B.
This work presents theoretical advances in the field of high-dimensional random matrix theory and, in particular, of relevance to the applied statistics community. Statistical distributions for the extreme eigenvalues of Jacobi random matrices are derived and, for the first time, we bridge the gap between exact (finite-dimensional) results and asymptotic results, providing finite-size corrections to the asymptotic results. These fundamental results find application in many cross-disciplinary problems including statistical hypothesis testing, multi-antenna wireless communication systems with co-channel interference and quantum conductance in mesoscopic physics.