Electronic Journal of Probability
- Electron. J. Probab.
- Volume 16 (2011), paper no. 90, 2481-2508.
High-Dimensional Random Geometric Graphs and their Clique Number
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.
Electron. J. Probab., Volume 16 (2011), paper no. 90, 2481-2508.
Accepted: 30 November 2011
First available in Project Euclid: 1 June 2016
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Devroye, Luc; György, András; Lugosi, Gábor; Udina, Frederic. High-Dimensional Random Geometric Graphs and their Clique Number. Electron. J. Probab. 16 (2011), paper no. 90, 2481--2508. doi:10.1214/EJP.v16-967. https://projecteuclid.org/euclid.ejp/1464820259