# Explicit universal minimal constants for polynomial growth of groups

@article{Lyons2022ExplicitUM, title={Explicit universal minimal constants for polynomial growth of groups}, author={Russell Lyons and Avinoam Mann and Romain Tessera and Matthew C. H. Tointon}, journal={Journal of Group Theory}, year={2022}, volume={0} }

Abstract Shalom and Tao showed that a polynomial upper bound on the size of a single, large enough ball in a Cayley graph implies that the underlying group has a nilpotent subgroup with index and degree of polynomial growth both bounded effectively. The third and fourth authors proved the optimal bound on the degree of polynomial growth of this subgroup, at the expense of making some other parts of the result ineffective. In the present paper, we prove the optimal bound on the degree of…

## One Citation

Locality of percolation for graphs with polynomial growth

- Mathematics
- 2022

Schramm’s Locality Conjecture asserts that the value of the critical percolation parameter p c of a graph satisfying p c < 1 depends only on its local structure. In this note, we prove this…

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