title: Truncations of random orthogonal matrices.
abstract: Statistical properties of nonsymmetric 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 nonorthogonality, 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.
authors.affiliation: Queen Mary University of London, School of Mathematical Sciences, London E1 4NS, United Kingdom.
authors.forename: Boris A
authors.initials: BA
authors.lastname: Khoruzhenko
authors.forename: Hans-Jürgen
authors.initials: HJ
authors.lastname: Sommers
authors.forename: Karol
authors.initials: K
authors.lastname: Życzkowski