@article{0fd4e8eec69e482fa819bc25c3c2d259,

title = "Fixed-point property of random groups",

abstract = "In this paper, using the generalized version of the theory of combinatorial harmonic maps, we give a criterion for a finitely generated group Γ to have the fixed-point property for a certain class of Hadamard spaces, and prove a fixed-point theorem for random-group actions on the same class of Hadamard spaces. We also study the existence of an equivariant energy-minimizing map from a Γ-space to the limit space of a sequence of Hadamard spaces with the isometric actions of a finitely generated group Γ. As an application, we present the existence of a constant which may be regarded as a Kazhdan constant for isometric discrete-group actions on a family of Hadamard spaces.",

keywords = "Finitely generated group, Fixed-point property, Hadamard space, Harmonic map, Random group, Rigidity",

author = "Hiroyasu Izeki and Takefumi Kondo and Shin Nayatani",

note = "Funding Information: Acknowledgements We thank Yann Ollivier for his instruction on the paper [10]. The first author is partly supported by the Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science. The second author is partly supported by the 21st Century COE Program of Research Institute for Mathematical Sciences, Kyoto University. The third author is partly supported by the Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science.",

year = "2009",

month = jun,

doi = "10.1007/s10455-008-9139-3",

language = "English",

volume = "35",

pages = "363--379",

journal = "Annals of Global Analysis and Geometry",

issn = "0232-704X",

publisher = "Springer Netherlands",

number = "4",

}