Distribution of the Smallest Eigenvalue in the Correlated Wishart Model

Understand

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 particularly interesting in many applications.
• In the complex and in the real case, we calculate it exactly for arbitrary empirical eigenvalues, i.e., for fully correlated Gaussian Wishart ensembles.
• To this end, we derive certain dualities of matrix models in ordinary space.