2020/10/06 by Benedikt Jahnel, Jahnel, Benedikt, András Tóbiás +1 · 1 citation
Mathematics · Social Sciences · #60G55 #60K35 #FOS: Mathematics #Human Mobility and Location-Based Analysis #Primary 82B43 #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #secondary 90B18
paper · pdf · doi:10.48550/arxiv.2010.03187
openalex publication_date 2020/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider undirected graphs that arise as deterministic functions of stationary point processes such that each point has degree bounded by two. For a large class of point processes and edge-drawing rules, we show that the arising graph has no infinite connected component, almost surely. In particular, this extends our previous result for SINR graphs based on stabilizing Cox point processes and verifies the conjecture of Balister and Bollobás that the bidirectional k-nearest neighbor graph of a two-dimensional homogeneous Poisson point process does not percolate for k=2.