Geodesic
Random walks and contracting elements II: Translation length and quasi-isometric embedding
Inhyeok Choi1 orcid
1Korea Institute for Advanced Study, Seoul, South Korea
Groups, geometry, and dynamics, Tome 19 (2025) no. 4, pp. 1373-1423

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DOI

Continuing from Choi (2022), we study random walks on metric spaces with contracting elements. We prove that random subgroups of the isometry group of a metric space are quasi-isometrically embedded into the space. We discuss this problem in two ways, namely in the sense of random walks and counting problem. We also establish the genericity of contracting elements and the central limit theorem and its converse for translation length.
DOI : 10.4171/ggd/831
Classification : 20F67, 30F60, 57M60, 60G50
Mots-clés : random walk, Outer space, Teichmüller space, CAT(0) space, central limit theorem, contracting property, quasi-isometric embedding

Inhyeok Choi  1

1 Korea Institute for Advanced Study, Seoul, South Korea 
Inhyeok Choi. Random walks and contracting elements II: Translation length and quasi-isometric embedding. Groups, geometry, and dynamics, Tome 19 (2025) no. 4, pp. 1373-1423. doi: 10.4171/ggd/831
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