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arXiv · 2203.12680

The $k$-Cap Process on Geometric Random Graphs

Mirabel Reid·Santosh S. Vempala
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Abstract

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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Mirabel Reid, Santosh S. Vempala. 2022-03-23. The $k$-Cap Process on Geometric Random Graphs. https://arxiv.org/abs/2203.12680

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