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High-Dimensional Random Geometric Graphs and their Clique Number

   
@article{EJP967,
	author = {Luc Devroye and András György and Gábor Lugosi and Frederic Udina},
	title = {High-Dimensional Random Geometric Graphs and their Clique Number},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {16},
	year = {2011},
	keywords = {Clique number; dependency testing; geometric graphs; random graphs},
	abstract = {We study the behavior of random geometric graphs in high dimensions. We show that as the dimension grows, the graph becomes similar to an Erdös-Rényi random graph. We pay particular attention to the clique number of such graphs and show that it is very close to that of the corresponding Erdös-Rényi graph when the dimension is larger than $\log^3(n)$ where $n$ is the number of vertices. The problem is motivated by a statistical problem of testing dependencies.},
	pages = {no. 90, 2481-2508},
	issn = {1083-6489},
	doi = {10.1214/EJP.v16-967},    
        url = {http://ejp.ejpecp.org/article/view/967}}