Correlations between zeros and supersymmetry

In our previous work [BSZ2], we proved that the correlation functions for s imultaneous zeros of random generalized polynomials have universal scaling, limits and we gave explicit formulas for pair correlations in codimensions 1 and 2. The purpose of this paper is to compute these universal limits in all dimensions and codimensions. First, we use a supersymmetry method to e xpress the n-point correlations as Berezin integrals. Then we use the Wick method to give a closed formula for the limit pair correlation function for the point case in all dimensions.