Truncations of Random Orthogonal Matrices

Abstract

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.

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

References in corpus (5)

• Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices
• Quantum-to-classical correspondence in open chaotic systems
• General Eigenvalue Correlations for the Real Ginibre Ensemble
• Characteristic polynomials in real Ginibre ensembles
• Distribution of resonances in the quantum open baker map