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Random Geometric Graphs beyond the Poisson process

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Combinatorics; Probability theory and stochastic processes

video/mp4

Author affiliation: Microsoft Research

2017-05-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61568

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/