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BIRS Workshop Lecture Videos

Random Geometric Graphs beyond the Poisson process Peres, Yuval


Random Geometric graphs have traditionally been considered on the nodes of a Poisson process, but recently there has been enhanced interest in more rigid point processes. We study continuum percolation for the Ginibre ensemble and the planar Gaussian zero process, which are the primary models of translation invariant point processes in 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 the infinite cluster in the supercritical regime. Finding suitable replacements for insertion and deletion tolerance is a crucial step. Joint work with Manju Krishnapur and Subhro Ghosh.

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