Correlations between zeros and supersymmetry

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.

13 pages, 1 figure

References in corpus (5)

• Distribution of zeros of random and quantum chaotic sections of positive line bundles
• Universality and scaling of correlations between zeros on complex manifolds
• Poincare-Lelong approach to universality and scaling of correlations between zeros
• Random almost holomorphic sections of ample line bundles on symplectic manifolds
• Universality and scaling of zeros on symplectic manifolds

Cited by in corpus (13)

• Critical points and supersymmetric vacua, III: String/M models
• Signed zeros of Gaussian vector fields-density, correlation functions and curvature
• Convergence of random zeros on complex manifolds
• Equilibrium distribution of zeros of random polynomials
• Asymptotics of polynomials and eigenfunctions
• Correlations between zeros of non-Gaussian random polynomials
• Two-Point Correlation Functions and Universality for the Zeros of Systems of SO(n+1)-invariant Gaussian Random Polynomials
• Asymptotics of partial density function vanishing along smooth subvariety
• Zeroes of random Reinhardt polynomials
• Smallest distances between zeros of Gaussian analytic functions
• Logarithmic Bergman kernel and Conditional expectation of Gaussian holomorphic fields
• Asymptotics of almost holomorphic sections of ample line bundles on symplectic manifolds: an addendum
• Random zeros on complex manifolds: conditional expectations