Continuum Percolation for Gaussian zeroes and Ginibre eigenvalues
Probability
2012-11-13 v1 Statistical Mechanics
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.
Keywords
Cite
@article{arxiv.1211.2514,
title = {Continuum Percolation for Gaussian zeroes and Ginibre eigenvalues},
author = {Subhro Ghosh and Manjunath Krishnapur and Yuval Peres},
journal= {arXiv preprint arXiv:1211.2514},
year = {2012}
}