The expression f(z) = \sum_i 1/(z-\lambda_i) is called Stieltjes transform and is heavily used in random matrix theory and similar expressions are used in other

The expression f(z) = \sum_i 1/(z-\lambda_i) is called Stieltjes transform and is heavily used in random matrix theory and similar expressions are used in other works such as Batson, Spielman and Srivastava. This is all to analyze the behavior of eigenvalues which is exactly what they were trying to understand. I'd be very surprised if Aaronson doesn't know about this.