  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. We prove:
  (i) convergence of condition numbers for bulk eigenvalues to an inverse Gamma
distribution; more generally, we decompose the quenched overlap (i.e.
conditioned on eigenvalues) as a product of independent random variables;
  (ii) asymptotic expectation of off-diagonal overlaps, both for microscopic or
mesoscopic separation of the corresponding eigenvalues;
  (iii) decorrelation of condition numbers associated to eigenvalues at
mesoscopic distance, at polynomial speed in the dimension;
  (iv) second moment asymptotics to identify the fluctuations order for
off-diagonal overlaps, when the related eigenvalues are separated by any
mesoscopic scale;
  (v) a new formula for the correlation between overlaps for eigenvalues at
microscopic distance, both diagonal and off-diagonal.
  These results imply estimates on the extreme condition numbers, the volume of
the pseudospectrum and the diffusive evolution of eigenvalues under Dyson-type
dynamics, at equilibrium.
