2012/02/06 by Anthony Mays, Mays, Anthony
Mathematics · Physics and Astronomy · #15B52 #Advanced Combinatorial Mathematics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR #msc:15B52
paper · pdf · doi:10.48550/arxiv.1202.1218
PhD thesis, submitted to the University of Melbourne, November 2011
arxiv created 2012/02/06 · openalex publication_date 2012/02/06 · arxiv updated 2012/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a five-step method for the calculation of eigenvalue correlation functions for various ensembles of real random matrices, based upon the method of (skew-) orthogonal polynomials. This scheme systematises existing methods and also involves some new techniques. The ensembles considered are: the Gaussian Orthogonal Ensemble (GOE), the real Ginibre ensemble, ensembles of partially symmetric real Gaussian matrices, the real spherical ensemble (of matrices A-1B), and the real anti-spherical ensemble (consisting of truncated real orthogonal matrices). Particular emphasis is paid to the variations in method required to treat odd-sized matrices. Various universality results are discussed, and a conjecture for an `anti-spherical law' is presented.