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arXiv · 2212.13199

Integral criteria of hyperbolicity for graphs and groups

Victor Gerasimov·Leonid Potyagailo
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Abstract

We establish three criteria of hyperbolicity of a graph in terms of ``average width of geodesic bigons''. In particular we prove that if the ratio of the Van Kampen area of a geodesic bigon $\beta$ and the length of $\beta$ in the Cayley graph of a finitely presented group $G$ is bounded above then $G$ is hyperbolic. We plan to use these results to characterize hyperbolic groups in terms of random walks.

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Victor Gerasimov, Leonid Potyagailo. 2022-12-26. Integral criteria of hyperbolicity for graphs and groups. https://arxiv.org/abs/2212.13199

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