caa a22 4500 475738705 CHVBK 20180406123453.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1007/s002220000092 doi (NATIONALLICENCE)springer-10.1007/s002220000092 Universality and scaling of correlations between zeros on complex manifolds [Elektronische Daten] [Pavel Bleher, Bernard Shiffman, Steve Zelditch] Abstract. : We study the limit as N→∞ of the correlations between simultaneous zeros of random sections of the powers L N of a positive holomorphic line bundle L over a compact complex manifold M, when distances are rescaled so that the average density of zeros is independent of N. We show that the limit correlation is independent of the line bundle and depends only on the dimension of M and the codimension of the zero sets. We also provide some explicit formulas for pair correlations. In particular, we prove that Hannay's limit pair correlation function for SU(2) polynomials holds for all compact Riemann surfaces. Springer-Verlag Berlin Heidelberg, 2000 Bleher Pavel Department of Mathematical Sciences, IUPUI, Indianapolis, IN 46202, USA¶(e-mail: bleher@math.iupui.edu), US aut Shiffman Bernard Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA¶(e-mail: shiffman@math.jhu.edu, zel@math.jhu.edu), US aut Zelditch Steve Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA¶(e-mail: shiffman@math.jhu.edu, zel@math.jhu.edu), US aut https://doi.org/10.1007/s002220000092 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s002220000092 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bleher Pavel Department of Mathematical Sciences, IUPUI, Indianapolis, IN 46202, USA¶(e-mail: bleher@math.iupui.edu), US aut NATIONALLICENCE 700 1- Shiffman Bernard Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA¶(e-mail: shiffman@math.jhu.edu, zel@math.jhu.edu), US aut NATIONALLICENCE 700 1- Zelditch Steve Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA¶(e-mail: shiffman@math.jhu.edu, zel@math.jhu.edu), US aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer