Correlations between zeros and supersymmetry
Mathematical Physics
2009-10-31 v2 Algebraic Geometry
Complex Variables
math.MP
Probability
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.
Keywords
Cite
@article{arxiv.math-ph/0011016,
title = {Correlations between zeros and supersymmetry},
author = {Pavel Bleher and Bernard Shiffman and Steve Zelditch},
journal= {arXiv preprint arXiv:math-ph/0011016},
year = {2009}
}
Comments
13 pages, 1 figure