Journal article

Spectral correlation functions of the sum of two independent complex Wishart matrices with unequal covariances

Gernot Akemann, Tomasz Checinski, Mario Kieburg

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | IOP PUBLISHING LTD | Published : 2016

Abstract

We compute the spectral statistics of the sum H of two independent complex Wishart matrices, each of which is correlated with a different covariance matrix. Random matrix theory enjoys many applications including sums and products of random matrices. Typically ensembles with correlations among the matrix elements are much more difficult to solve. Using a combination of supersymmetry, superbosonisation and bi-orthogonal functions we are able to determine all spectral k-point density correlation functions of H for arbitrary matrix size N. In the half-degenerate case, when one of the covariance matrices is proportional to the identity, the recent results by Kumar for the joint eigenvalue distri..

View full abstract

University of Melbourne Researchers

Grants

Awarded by German Research Council DFG


Funding Acknowledgements

We thank Santosh Kumar for fruitful discussions. Financial support through LabEx PALM (G A), FSPM<SUP>2</SUP> (T C) and CRC 701: Spectral Structures and Topological Methods in Mathematics of the German Research Council DFG (M K) are gratefully acknowledged. Two of us (G A and T C) would like to kindly thank the LPTMS in Orsay for hospitality where part of this work was established.