2010/08/31 by Boris A. Khoruzhenko, Hans-Juergen Sommers, Karol Zyczkowski · 1 citation
Physics and Astronomy · Mathematics · #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1103/physreve.82.040106
published as Phys. Rev. E 82, 040106(R) (2010) [4 pages] · 4 pages, final revised version (one reference added, minor changes in Introduction)
arxiv created 2010/10/20 · arxiv updated 2010/10/21
Statistical properties of non--symmetric real random matrices of size M, obtained as truncations of random orthogonal N× 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.