Recursion scheme for the largest beta-Wishart-Laguerre eigenvalue and Landauer conductance in quantum transport
Peter J Forrester, Santosh Kumar
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | IOP PUBLISHING LTD | Published : 2019
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 ..View full abstract
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Awarded by ARC
Awarded by SERB, DST, Government of India
PJF acknowledges support from the Australian Research Council (ARC) through the ARC Centre of Excellence for Mathematical and Statistical frontiers (ACEMS) and ARC grant DP170102028. SK acknowledges the support by the grant EMR/2016/000823 provided by SERB, DST, Government of India. Comments by Mario Kieburg on an earlier draft of the manuscript are appreciated.