We give a characterization of vertex-monotone properties with sharp thresholds in a Poisson random geometric graph or hypergraph. As an application we show that a geometric model of random k-SAT exhibits a sharp threshold for satisfiability.
@InProceedings{bradonjic_et_al:LIPIcs.APPROX-RANDOM.2014.500, author = {Bradonjic, Milan and Perkins, Will}, title = {{On Sharp Thresholds in Random Geometric Graphs}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)}, pages = {500--514}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-74-3}, ISSN = {1868-8969}, year = {2014}, volume = {28}, editor = {Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.500}, URN = {urn:nbn:de:0030-drops-47195}, doi = {10.4230/LIPIcs.APPROX-RANDOM.2014.500}, annote = {Keywords: Sharp thresholds, random geometric graphs, k-SAT} }
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