Open Access
September 2016 Continuum percolation for Gaussian zeroes and Ginibre eigenvalues
Subhroshekhar Ghosh, Manjunath Krishnapur, Yuval Peres
Ann. Probab. 44(5): 3357-3384 (September 2016). DOI: 10.1214/15-AOP1051


We study continuum percolation on certain negatively dependent point processes on $\mathbb{R}^{2}$. Specifically, we study the Ginibre ensemble and the planar Gaussian zero process, which are the two main natural models of translation invariant point processes on the plane exhibiting local repulsion. For the Ginibre ensemble, we establish the uniqueness of infinite cluster in the supercritical phase. For the Gaussian zero process, we establish that a non-trivial critical radius exists, and we prove the uniqueness of infinite cluster in the supercritical regime.


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Subhroshekhar Ghosh. Manjunath Krishnapur. Yuval Peres. "Continuum percolation for Gaussian zeroes and Ginibre eigenvalues." Ann. Probab. 44 (5) 3357 - 3384, September 2016.


Received: 1 November 2013; Revised: 1 July 2015; Published: September 2016
First available in Project Euclid: 21 September 2016

zbMATH: 1375.60037
MathSciNet: MR3551199
Digital Object Identifier: 10.1214/15-AOP1051

Primary: 60D05 , 60G55 , 60K35
Secondary: 62P30

Keywords: Boolean percolation , continuum percolation , Gaussian zeroes , Ginibre ensemble , hole probabilities , Stochastic geometry

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 5 • September 2016
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