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Correlations between zeros and supersymmetry

Pavel Bleher·Bernard Shiffman·Steve Zelditch
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Abstract

In our previous work [math-ph/9904020], 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.

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Pavel Bleher, Bernard Shiffman, Steve Zelditch. 2000-11-20. Correlations between zeros and supersymmetry. https://doi.org/10.1007/s002200100512

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