Volume 109, Number 2, January 2015
|Number of page(s)||6|
|Published online||04 February 2015|
Limiting statistics of the largest and smallest eigenvalues in the correlated Wishart model
1 Fakultät für Physik, Universität Duisburg-Essen - 47048 Duisburg, Germany
2 Fakultät für Physik, Universität Bielefeld - 33501 Bielefeld, Germany
Received: 17 October 2014
Accepted: 16 January 2015
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 empirically much more important real case still poses substantial challenges. We put forward a new approach, which maps arbitrary statistical quantities, depending on invariants only, to invariant Hermitian matrix models. For completeness we also include the quaternion case and deal with all three cases in a unified way. As an important application, we study the statistics of the largest eigenvalue and its limiting distributions in the correlated Wishart model, because they help to estimate the behavior of large complex systems. We show that even for fully correlated Wishart ensembles, the Tracy-Widom distribution can be the limiting distribution of the largest as well as the smallest eigenvalue, provided that a certain scaling of the empirical eigenvalues holds.
PACS: 05.45.Tp – Time series analysis / 02.50.-r – Probability theory, stochastic processes, and statistics / 02.20.-a – Group theory
© EPLA, 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.