Resumen de Continuum percolation for Gaussian zeroes and Ginibre eigenvalues

Subhroshekhar Ghosh, Manjunath Krishnapur, Yuval Peres

• 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.