Volume Entropy Rigidity for Random Groups at Low Densities
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912402276089856 |
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| author | Hua, Dongming |
| author_facet | Hua, Dongming |
| contents | We study the rigidity of the volume entropy for weighted word metrics on hyperbolic groups, building on a recent convexity result due to Cantrell-Tanaka. Using ideas from small cancellation theory, we give conditions under which a hyperbolic group admits a unique normalized weight minimizing the entropy. Moreover, we show that these conditions are generic for random groups at small densities, and that the unique minimizer of such a generic group is arbitrarily close to the uniform weight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Volume Entropy Rigidity for Random Groups at Low Densities Hua, Dongming Group Theory Metric Geometry We study the rigidity of the volume entropy for weighted word metrics on hyperbolic groups, building on a recent convexity result due to Cantrell-Tanaka. Using ideas from small cancellation theory, we give conditions under which a hyperbolic group admits a unique normalized weight minimizing the entropy. Moreover, we show that these conditions are generic for random groups at small densities, and that the unique minimizer of such a generic group is arbitrarily close to the uniform weight. |
| title | Volume Entropy Rigidity for Random Groups at Low Densities |
| topic | Group Theory Metric Geometry |
| url | https://arxiv.org/abs/2505.23364 |