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# Integral criteria of hyperbolicity for graphs and groups

Dec 2022

We establish three criteria of hyperbolicity of a graph in terms of averagewidth of geodesic bigons''. In particular we prove that if the ratio of the VanKampen area of a geodesic bigon $\beta$ and the length of $\beta$ in the Cayleygraph of a finitely presented group $G$ is bounded above then $G$ ishyperbolic. We plan to use these results to characterize hyperbolic groups in terms ofrandom walks.

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