Correlations between zeros and supersymmetry

Pavel Bleher*, Bernard Shiffman, Steve Zelditch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)255-269
Number of pages15
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - 2001

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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