, Volume 224, Issue 1, pp 255-269
Date: 25 Jan 2014

Correlations Between Zeros and Supersymmetry

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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.

Received: 13 November 2000 / Accepted: 23 February 2001