The distribution of overlaps between eigenvectors of Ginibre matrices

Understand

We study the overlaps between eigenvectors of nonnormal matrices.

• They quantify the stability of the spectrum, and characterize the joint eigenvalues increments under Dyson-type dynamics.
• Well known work by Chalker and Mehlig calculated the expectation of these overlaps for complex Ginibre matrices.
• For the same model, we extend their results by deriving the distribution of diagonal overlaps (the condition numbers), and their correlations.