The homology torsion growth of determinantal hypertrees
Abstract
Abstract Fix a dimension $$d\ge 2$$ d ≥ 2 , and let $$T_n$$ T n be a random d -dimensional determinantal hypertree on n vertices. We prove that $$\begin{aligned} \frac{\log |H_{d-1}(T_n,\mathbb {Z})|}{{{n\atopwithdelims (){d}}}} \end{aligned}$$ log | H d - 1 ( T n , Z ) | n d converges in probability to a constant $$c_d$$ c d , which satisfies $$\begin{aligned} \frac{1}{2} \log \left( \frac{d+1}{e}\right) \le c_d\le \frac{1}{2} \log \left( d+1\right) . \end{aligned}$$ 1 2 log d + 1 e ≤ c d ≤ 1 2 log d + 1 .
Fields of Study & Subjects
Advanced Topics in Algebra
Publication details
- Journal / source
- Mathematische Annalen
- Volume
- 395
- Issue
- 3
- Publication date
- 7 May 2026
- Language
- EN