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15 July 2017 Rigidity and tolerance in point processes: Gaussian zeros and Ginibre eigenvalues
Subhroshekhar Ghosh, Yuval Peres
Duke Math. J. 166(10): 1789-1858 (15 July 2017). DOI: 10.1215/00127094-2017-0002


Let Π be a translation-invariant point process on the complex plane C, and let DC be a bounded open set. We ask the following: What does the point configuration Πout obtained by taking the points of Π outside D tell us about the point configuration Πin of Π inside D? We show that, for the Ginibre ensemble, Πout determines the number of points in Πin. For the translation-invariant zero process of a planar Gaussian analytic function, we show that Πout determines the number as well as the center of mass of the points in Πin. Further, in both models we prove that the outside says “nothing more” about the inside, in the sense that the conditional distribution of the inside points, given the outside, is mutually absolutely continuous with respect to the Lebesgue measure on its supporting submanifold.


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Subhroshekhar Ghosh. Yuval Peres. "Rigidity and tolerance in point processes: Gaussian zeros and Ginibre eigenvalues." Duke Math. J. 166 (10) 1789 - 1858, 15 July 2017.


Received: 31 July 2013; Revised: 28 April 2015; Published: 15 July 2017
First available in Project Euclid: 9 May 2017

zbMATH: 06773293
MathSciNet: MR3679882
Digital Object Identifier: 10.1215/00127094-2017-0002

Primary: 60G55
Secondary: 60B20

Keywords: Determinantal point processes , Gaussian analytic functions , Ginibre ensemble , Point processes , Random eigenvalues , random matrices , random polynomials , random spectra , random zeros , rigidity , statistical mechanics

Rights: Copyright © 2017 Duke University Press


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Vol.166 • No. 10 • 15 July 2017
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