  In this paper we prove that as N goes to infinity, the scaling limit of the
correlation between critical points z1 and z2 of random holomorphic sections of
the N-th power of a positive line bundle over a compact Riemann surface tends
to 2/(3pi^2) for small sqrt(N)|z1-z2|. The scaling limit is directly calculated
using a general form of the Kac-Rice formula and formulas and theorems of Pavel
Bleher, Bernard Shiffman, and Steve Zelditch.
