## Random Gromov’s monsters do not act non-elementarily on hyperbolic spaces

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- by Dominik Gruber, Alessandro Sisto and Romain Tessera PDF
- Proc. Amer. Math. Soc.
**148**(2020), 2773-2782

## Abstract:

We show that Gromov’s monster groups arising from i.i.d. labelings of expander graphs do not admit non-elementary actions on geodesic hyperbolic spaces. The proof relies on comparing properties of random walks on randomly labeled graphs and on groups acting non-elementarily on hyperbolic spaces.## References

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## Additional Information

**Dominik Gruber**- Affiliation: Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
- MR Author ID: 1089843
- Email: dominik.gruber@math.ethz.ch
**Alessandro Sisto**- Affiliation: Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
- MR Author ID: 881750
- Email: sisto@math.ethz.ch
**Romain Tessera**- Affiliation: Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, F-91405 Orsay, France
- MR Author ID: 800491
- Email: tessera@phare.normalesup.org
- Received by editor(s): June 6, 2017
- Received by editor(s) in revised form: March 13, 2019, and May 17, 2019
- Published electronically: March 18, 2020
- Communicated by: Kenneth Bromberg
- © Copyright 2020 Dominik Gruber, Alessandro Sisto, and Romain Tessera
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 2773-2782 - MSC (2010): Primary 20F65
- DOI: https://doi.org/10.1090/proc/14754
- MathSciNet review: 4099767