The k-Cap Process on Geometric Random Graphs
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The k-cap (or k-winners-take-all) process on a graph works as follows: in each iteration, exactly k vertices of the graph are in the cap (i.e., winners); the next round winners are the vertices that have the highest total degree to the current winners, with ties broken randomly. This natural process is a simple model of firing activity in the brain. We study its convergence on geometric random graphs, revealing rather surprising behavior.
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