Joon-Hyeok Yim

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math.PR2026

A quantitative tree-likeness bound from average hyperbolicity

Joon-Hyeok Yim

Chatterjee and Sloman proved that a bounded measurable similarity function with sufficiently small average Gromov hyperbolicity admits a tree representation with small mean approxi…

math.PR2024

Hyperbolicity, slimness, and minsize, on average

Anna C. Gilbert, Joon-Hyeok Yim

A metric space $(X, d)$ is said to be $δ$ -hyperbolic if $d (x, y) + d (z, w)$ is at most $max (d (x, z) + d (y, w), d (x, w) + d (y, z))$ by $2 δ$ . A geodesic space is $δ$ -slim if every geodesic tria…