2014/12/09 by Daniel Waltner, Tim Wirtz, Thomas Guhr · 11 citations
Computer Science · Mathematics · Physics and Astronomy · #Correlation #Eigenvalues and eigenvectors #Expression (computer science) #Limit (mathematics) #Probability density function #Quantum Information and Cryptography #Random Matrices and Applications #Statistical Mechanics and Entropy #Wishart distribution #math-ph #math.MP #math.ST #stat.TH
paper · pdf · doi:10.1088/1751-8113/48/17/175204
published in Journal of Physics A Mathematical and Theoretical 48(17), 175204 (Institute of Physics) · 16 pages, 3 figures
arxiv created 2014/12/09 · openalex publication_date 2015/04/08 · arxiv updated 2015/05/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Data sets collected at different times and different observing points can possess correlations at different times and at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density of the Wishart correlation matrices using supersymmetry. In the complex case we obtain a new closed form expression which we compare to previous results in the literature. In the more relevant and much more complicated real case we derive an expression for the density in terms of a fourfold integral. Finally, we calculate the density in the limit of large correlation matrices.