Continuum percolation for Gaussian zeroes and Ginibre eigenvalues

• Subhroshekhar Ghosh ^[2] ; Manjunath Krishnapur ^[3] ; Yuval Peres ^[1]
  1. [1] The Microsoft Research - University of Trento Centre for Computational and Systems Biology

     The Microsoft Research - University of Trento Centre for Computational and Systems Biology

     Trento, Italia

     
  2. [2] Princenton University
  3. [3] Indian Institute of Science

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 5, 2016, págs. 3357-3384
• Idioma: inglés
• DOI: 10.1214/15-AOP1051
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• Resumen

  • We study continuum percolation on certain negatively dependent point processes on R2R2. 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.