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arXiv · 2505.23364

Volume Entropy Rigidity for Random Groups at Low Densities

Dongming Hua
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Abstract

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.

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Dongming Hua. 2025-05-29. Volume Entropy Rigidity for Random Groups at Low Densities. https://arxiv.org/abs/2505.23364

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