Journal article

Universal microscopic correlation functions for products of truncated unitary matrices

Gernot Akemann, Zdzislaw Burda, Mario Kieburg, Taro Nagao

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | IOP PUBLISHING LTD | Published : 2014

Abstract

We investigate the spectral properties of the product of M complex non-Hermitian random matrices that are obtained by removing L rows and columns of larger unitary random matrices uniformly distributed on the group U(N + L). Such matrices are called truncated unitary matrices or random contractions. We first derive the joint probability distribution for the complex eigenvalues of the product matrix for fixed N, L, and M, given by a standard determinantal point process in the complex plane. The weight however is non-standard and can be expressed in terms of the Meijer G-function. The explicit knowledge of all eigenvalue correlation functions and the corresponding kernel allows us to take vari..

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University of Melbourne Researchers

Grants

Awarded by 'Symmetries and Universality in Mesoscopic Systems of the German research council DFG


Awarded by National Centre of Science in Poland


Awarded by Japan Society for the Promotion of Science (KAKENHI)


Funding Acknowledgements

We acknowledge partial support by the SFB vertical bar TR12 'Symmetries and Universality in Mesoscopic Systems' of the German research council DFG (GA), by the Alexander von Humboldt Foundation (ZB and MK), by the grant no DEC-2011/02/A/ST1/00119 of National Centre of Science in Poland (ZB) and by the Japan Society for the Promotion of Science (KAKENHI 20540372 and 25400397) (TN). ZB especially thanks Bielefeld University for its hospitality.