Groups of given intermediate word growth

By Laurent Bartholdi, A. Erschler. 2011

51 citations recorded by the source corpus.

We show that there exists a finitely generated group of growth ~f for all functions f:\mathbb{R}\rightarrow\mathbb{R} satisfying f(2R) \leq f(R)^{2} \leq f(\eta R) for all R large enough and \eta\approx2.4675 the positive root of X^{3}-X^{2}-2X-4. This covers all functions that grow uniformly faster than \exp(R^{\log2/\log\eta}). We also give a family of self-similar branched groups of growth ~\exp(R^\alpha) for a dense set of \alpha\in(\log2/\log\eta,1).

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cffe56aa18bf2a519d1b828a2d5b5d39c59b3454

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In Computational Theory and Mathematics

1. Jérémie Brieussel
2. Tianyi Zheng

In Geometry and Topology

1. Jérémie Brieussel
2. Tianyi Zheng

Citations in the corpus

• Speed of random walks, isoperimetry and compression of finitely generated groups (2015, background): “[13] Bartholdi, Laurent; Erschler, Anna, Groups of given intermediate word growth, Ann.”