The Annals of Probability

Continuum percolation for Gaussian zeroes and Ginibre eigenvalues

Subhroshekhar Ghosh, Manjunath Krishnapur, and Yuval Peres

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Abstract

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.

Article information

Source
Ann. Probab., Volume 44, Number 5 (2016), 3357-3384.

Dates
Received: November 2013
Revised: July 2015
First available in Project Euclid: 21 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.aop/1474462100

Digital Object Identifier
doi:10.1214/15-AOP1051

Mathematical Reviews number (MathSciNet)
MR3551199

Zentralblatt MATH identifier
1375.60037

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60G55: Point processes 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 62P30: Applications in engineering and industry

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

Citation

Ghosh, Subhroshekhar; Krishnapur, Manjunath; Peres, Yuval. Continuum percolation for Gaussian zeroes and Ginibre eigenvalues. Ann. Probab. 44 (2016), no. 5, 3357--3384. doi:10.1214/15-AOP1051. https://projecteuclid.org/euclid.aop/1474462100


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