High-dimensional random geometric graphs and their clique number
Luc Devroye, Andras Gyorgy, Gábor Lugosi and Frederic Udina
Electronic Journal of Probability Volume 16, pp. 2481-2508, 2011.

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 Erd ̋os-R ́enyi 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 Erd ̋os-R ́enyi graph when the dimension is larger than log3 n where n is the number of vertices. The problem is motivated by a statistical problem of testing dependencies.

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