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CONTINUUM PERCOLATION FOR GAUSSIAN ZEROES AND GINIBRE EIGENVALUES

Ghosh, Subhroshekhar and Krishnapur, Manjunath and Peres, Yuval (2016) CONTINUUM PERCOLATION FOR GAUSSIAN ZEROES AND GINIBRE EIGENVALUES. In: ANNALS OF PROBABILITY, 44 (5). pp. 3357-3384.

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Official URL: http://dx.doi.org/10.1214/15-AOP1051

Abstract

We study continuum percolation on certain negatively dependent point processes on 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.

Item Type: Journal Article
Additional Information: Copy right for this aticle belongs to the INST MATHEMATICAL STATISTICS, 3163 SOMERSET DR, CLEVELAND, OH 44122 USA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 03 Dec 2016 06:26
Last Modified: 03 Dec 2016 06:26
URI: http://eprints.iisc.ac.in/id/eprint/55282

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