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arXiv · 2506.14219

The VC-dimension of random subsets of finite groups

Brad Rodgers·Anurag Sahay
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Abstract

For a random subset of a finite group $G$ of cardinality $N$, we consider the VC-dimension of the family of its translates (equivalently the VC-dimension of a random Cayley graph) and prove a law of large numbers as $N\rightarrow\infty$. This answers a question of McDonald--Sahay--Wyman.

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Brad Rodgers, Anurag Sahay. 2026-08-14. The VC-dimension of random subsets of finite groups. https://arxiv.org/abs/2506.14219

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