In random geometric graphs, the threshold radius for maximum degree has compound Poisson limits when the degree is bounded and Poisson limits when it diverges slower than log n, with corresponding limiting point configurations for the high-degree vertices.
Random Geometric Graphs
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Limit distributions of the threshold radius for the maximum degree and the associated point configurations in random geometric graphs
In random geometric graphs, the threshold radius for maximum degree has compound Poisson limits when the degree is bounded and Poisson limits when it diverges slower than log n, with corresponding limiting point configurations for the high-degree vertices.