Truncations of random unitary matrices

Details Truncations of random unitary matrices Truncations of random unitary matrices

1999-10-21

arxiv.org/abs/chao-dyn/9910032v3

J.Phys. A33 (2000) 2045-2057

Physics

Condensed Matter

9 pages in RevTex with 7 pictures in .ps (included) version 3, some misprints corrected

Scientific paper

10.1088/0305-4470/33/10/307

We analyze properties of non-hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N>M, distributed according to the Haar measure. In this way we define ensembles of random matrices and study the statistical properties of the spectrum located inside the unit circle. In the limit of large matrices, this ensemble is characterized by the ratio M/N. For the truncated CUE we derive analytically the joint density of eigenvalues from which easily all correlation functions are obtained. For N-M fixed and N--> infinity the universal resonance-width distribution with N-M open channels is recovered.

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