We study the behavior of random geometric graphs in high dimensions. We show that as the dimension grows, the graph becomes similar to an Erds-Rnyi 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 Erds-Rnyi 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..
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Devroye et al. (2011) studied this question.
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