### Abstract

We show a fixed-point property of certain random groups for a wide class of CAT.0/ spaces. The model of random groups under consideration is given as the set of presentations .S;R/, where S is a generating set and the set of relations R is a subset of the set of all plain words of the same length with suitably fixed density. Our main theorem says that, with high probability, groups obtained by such presentations have the fixed-point property for all CAT.0/ spaces having bounded singularities.

Original language | English |
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Pages (from-to) | 1101-1140 |

Number of pages | 40 |

Journal | Groups, Geometry, and Dynamics |

Volume | 8 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

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### Keywords

- CAT(0) spaces
- Fixed-point property
- Harmonic maps
- Random groups

### ASJC Scopus subject areas

- Geometry and Topology
- Discrete Mathematics and Combinatorics