Truncations of Random Orthogonal Matrices

Details Truncations of Random Orthogonal Matrices Truncations of Random Orthogonal Matrices

2010-08-12

arxiv.org/abs/1008.2075v2

Phys. Rev. E 82, 040106(R) (2010) [4 pages]

Physics

Condensed Matter

Statistical Mechanics

4 pages, final revised version (one reference added, minor changes in Introduction)

Scientific paper

10.1103/PhysRevE.82.040106

Statistical properties of non--symmetric real random matrices of size $M$, obtained as truncations of random orthogonal $N\times N$ matrices are investigated. We derive an exact formula for the density of eigenvalues which consists of two components: finite fraction of eigenvalues are real, while the remaining part of the spectrum is located inside the unit disk symmetrically with respect to the real axis. In the case of strong non--orthogonality, $M/N=$const, the behavior typical to real Ginibre ensemble is found. In the case $M=N-L$ with fixed $L$, a universal distribution of resonance widths is recovered.

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