Recursion scheme for the largest beta-Wishart-Laguerre eigenvalue and Landauer conductance in quantum transport

Abstract

The largest eigenvalue distribution of the Wishart?Laguerre ensemble, indexed by Dyson parameter and Laguerre parameter a, is fundamental in multivariate statistics and finds applications in diverse areas. Based on a generalisation of the Selberg integral, we provide an effective recursion scheme to compute this distribution explicitly in both the original model, and a fixed-trace variant, for a, non-negative integers and finite matrix size. For = 2 this circumvents known symbolic evaluation based on determinants which become impractical for large dimensions. Our exact results have immediate applications in the areas of multiple channel communication and bipartite entanglement. Moreover, we ..