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arXiv · 2607.25578

Growth gaps and exponential genericity in acylindrically hyperbolic groups

Lihuang Ding·Wenyuan Yang
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Abstract

We prove that, for every finite generating set of an acylindrically hyperbolic group, the set of non-WPD elements has strictly smaller exponential growth rate. Equivalently, WPD elements are exponentially generic. As applications, we prove growth tightness and cogrowth tightness for acylindrically hyperbolic groups.

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Lihuang Ding, Wenyuan Yang. 2026-07-28. Growth gaps and exponential genericity in acylindrically hyperbolic groups. https://arxiv.org/abs/2607.25578

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