Communications in Mathematical Physics

, Volume 224, Issue 1, pp 255–269

Correlations Between Zeros and Supersymmetry

  • Pavel Bleher
  • Bernard Shiffman
  • Steve Zelditch
Article

DOI: 10.1007/s002200100512

Cite this article as:
Bleher, P., Shiffman, B. & Zelditch, S. Commun. Math. Phys. (2001) 224: 255. doi:10.1007/s002200100512

Abstract:

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Pavel Bleher
    • 1
  • Bernard Shiffman
    • 2
  • Steve Zelditch
    • 2
  1. 1.Department of Mathematical Sciences, IUPUIIndianapolisUSA
  2. 2.Department of Mathematics, Johns Hopkins UniversityBaltimoreUSA

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