Communications in Mathematical Physics

, Volume 224, Issue 1, pp 255-269

Correlations Between Zeros and Supersymmetry

  • Pavel BleherAffiliated withDepartment of Mathematical Sciences, IUPUI
  • , Bernard ShiffmanAffiliated withDepartment of Mathematics, Johns Hopkins University
  • , Steve ZelditchAffiliated withDepartment of Mathematics, Johns Hopkins University

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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.