Numerical and Monte Carlo verification of V-distribution
Ronaldo Dias, Vyacheslav L. Girko · Random Operators and Stochastic Equations · 1998
It is shown that V -distribution is a valid probability density for all values of parameters and approximates the empirical density of eigenvalues of certain random non symmetrical matrices. 1. INTRODUCTION Random matrix physics is generally thought to consist of the following subfields: 1. Statistical properties of nuclear and atomic spectra. Time reversal symmetry braking and the field theory of quantum chaos [1-51]. 2. Quantum chaology and condensed matter physics. 3. Dissipative quantum dynamics. 4. Another rather broad field of the random matrices theory applications is related to quantum field theory: the large limit of QCD, two dimensional (2D) quantum gravity and bosonic strings. 5. Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering: Random matrix approach for systems with broken time-reversal invariance. For data of the complete spin and parity, the symmetric and unitary matrix of scattering can be written in the form: S = U ~ SU T ; ...