Correlations between zeros and supersymmetry

Details Correlations between zeros and supersymmetry Correlations between zeros and supersymmetry

2000-11-10

arxiv.org/abs/math-ph/0011016v2

Commun. Math. Phys. 224 (2001), 255--269.

Physics

Mathematical Physics

13 pages, 1 figure

Scientific paper

10.1007/s002200100512

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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