# Banach Zuk's criterion for partite complexes with application to random groups

@inproceedings{Oppenheim2021BanachZC, title={Banach Zuk's criterion for partite complexes with application to random groups}, author={Izhar Oppenheim}, year={2021} }

We prove a Banach version of Żuk’s criterion for groups acting on partite simplicial complexes. Using this new criterion we derive a new fixed point theorem for random groups in the Gromov density model with respect to several classes of Banach spaces (L spaces, Hilbertian spaces, uniformly curved spaces). In particular, we show that for every p, a group in the Gromov density model has asymptotically almost surely property (FL) and give a sharp lower bound for the growth of the conformal…

## 2 Citations

### Round Trees and Conformal Dimension in Random Groups: low density to high density

- Mathematics
- 2022

We investigate conformal dimension for the class of inﬁnite hyperbolic groups in the Gromov density model G dm,l of random groups with m ≥ 2 ﬁxed generators, density 0 < d < 1 / 2 and relator length…

### Random groups do not have Property (T) at densities below 1/4

- Mathematics
- 2022

We prove that random groups in the Gromov density model at density d < 1 / 4 do not have Property (T), answering a conjecture of Przytycki. We also prove similar results in the k -angular model of…

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