Correlations Between Zeros and Supersymmetry
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- Bleher, P., Shiffman, B. & Zelditch, S. Commun. Math. Phys. (2001) 224: 255. doi:10.1007/s002200100512
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In our previous work [BSZ2], we proved that the correlation functions for simultaneous 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 express 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.