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Random subgroup is quasi-isometrically embedded

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Inhyeok Choi (KAIST)

Abstract: Consider N independent non-elementary random walks on the isometry group of a Gromov hyperbolic space. We can then ask the nature of the subgroup generated by the N isometries arising at step n. Taylor and Tiozzo proved that this subgroup is free and is quasi-isometrically embedded into the ambient space via the orbit map for asymptotic probability 1. In this talk, I will explain how the recently developed theories of Gouëzel and Baik-Choi-Kim applies to this problem. This approach provides further information on the asymptotic probability and generalizes the setting to include CAT(0) spaces.