Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $k$-Cap Process on Geometric Random Graphs   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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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex