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Asymptotic Coincidence of the Statistics for Degenerate and Non-Degenerate Correlated Real Wishart Ensembles
Tim Wirtz, Mario Kieburg, Thomas Guhr
The correlated Wishart model provides the standard benchmark when analyzing time series of any kind. Unfortunately, the real case, which is the most relevant one in applications, p…
The Smallest Eigenvalue Distribution in the Real Wishart-Laguerre Ensemble with Even Topology
Tim Wirtz, Gernot Akemann, Thomas Guhr +2
We consider rectangular random matrices of size belonging to the real Wishart-Laguerre ensemble also known as the chiral Gaussian orthogonal ensemble. This ensemble app…
Eigenvalue Density of the Doubly Correlated Wishart Model: Exact Results
Daniel Waltner, Tim Wirtz, Thomas Guhr
Data sets collected at different times and different observing points can possess correlations at different times at different positions. The doubly correlated Wishart model…
Limiting Statistics of the Largest and Smallest Eigenvalues in the Correlated Wishart Model
Tim Wirtz, Mario Kieburg, Thomas Guhr
The correlated Wishart model provides a standard tool for the analysis of correlations in a rich variety of systems. Although much is known for complex correlation matrices, the em…
Completing the picture for the smallest eigenvalue of real Wishart matrices
G. Akemann, T. Guhr, M. Kieburg +2
Rectangular real matrices with a Gaussian distribution appear very frequently in data analysis, condensed matter physics and quantum field theory. A central…
Distribution of the Smallest Eigenvalue in Complex and Real Correlated Wishart Ensembles
Tim Wirtz, Thomas Guhr
For the correlated Gaussian Wishart ensemble we compute the distribution of the smallest eigenvalue and a related gap probability.We obtain exact results for the complex (β=2) and…
Distribution of the Smallest Eigenvalue in the Correlated Wishart Model
Tim Wirtz, Thomas Guhr
Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is part…