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We present geometric conditions on a metric space $(Y,d_Y)$ ensuring that almost surely, any isometric action on $Y$ by Gromov's expander-based random group has a common fixed point.
On the moduli of convexity and smoothness
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1 1 -cohomologie des représentations unitaires des groupes de Lie semi-simples et résolubles. Produits tensoriels continus de représentations
P. Delorme · 1977
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Étude de la l l -cohomologie et de la topologie du dual pour les groupes de Lie à radical abélien
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Modern dimension theory
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P. Pansu · 1995
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J. Jost · 1997
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Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings
B. Kleiner and B. Leeb · 1997
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On embedding expanders into l p l_{p} spaces
J. Matoušek · 1997
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A fixed point theorem of discrete group actions on Riemannian manifolds
M.-T. Wang · 1998
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Metric spaces of non-positive curvature
M. R. Bridson and A. Haefliger · 1999
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The probabilistic method
N. Alon and J. H. Spencer · 2000
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Counterexamples to the Baum-Connes conjecture
N. Higson, V. Lafforgue, and G. Skandalis · 2002
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Random walk in random groups
M. Gromov · 2003
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Addendum to: “Random walk in random groups” [Geom. Funct. Anal. 13
L. Silberman · 2003
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Property (T) and Kazhdan constants for discrete groups
A. Żuk · 2003
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A note on non-amenability of ℬ ( l p ) {\mathscr{B}}(l_{p}) for p = 1 , 2 p=1,2
N. Ozawa · 2004
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On metric Ramsey type phenomena
Y. Bartal, N. Linial, M. Mendel, and A. Naor · 2005
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Almost isometric actions, property (T), and local rigidity
D. Fisher and G. Margulis · 2005
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A January 2005 invitation to random groups
Y. Ollivier · 2005
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Hyperbolic groups admit proper affine isometric actions on l p l^{p} -spaces
G. Yu · 2005
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Expander graphs and their applications
S. Hoory, N. Linial, and A. Wigderson · 2006
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Markov chains in smooth Banach spaces and Gromov-hyperbolic metric spaces
A. Naor, Y. Peres, O. Schramm, and S. Sheffield · 2006
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On a small cancellation theorem of Gromov
Y. Ollivier · 2006
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Fixed points of actions of building groups on CAT(0) spaces
P. Pansu · 2006
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The Novikov conjecture for linear groups
E. Guentner, N. Higson, and S. Weinberger · 2005
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Combinatorial harmonic maps and discrete-group actions on Hadamard spaces
H. Izeki and S. Nayatani · 2005
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Representations of polygons of finite groups
M. Kapovich · 2005
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Nagata dimension, quasisymmetric embeddings, and Lipschitz extensions
U. Lang and T. Schlichenmaier · 2005
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Metric structures in L 1 {L}_{1} : Dimension, snowflakes, and average distortion
J. R. Lee, M. Mendel, and A. Naor · 2005
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Extending Lipschitz functions via random metric partitions
J. R. Lee and A. Naor · 2005
Cited alongside, same era.
Property (T) and rigidity for actions on Banach spaces
U. Bader, A. Furman, T. Gelander, and N. Monod · 2007
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A topological Tits alternative
E. Breuillard and T. Gelander · 2007
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Kazhdan groups with infinite outer automorphism group
Y. Ollivier and D. T. Wise · 2007
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Examples of random groups
G. A. Arzhantseva and T. Delzant · 2008
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Groups not acting on manifolds
D. Fisher and L. Silberman · 2008
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Infinite groups with fixed point properties
G. Arzhantseva, M. R. Bridson, T. Januszkiewicz, I. J. Leary, A. Minasyan, and J. Świa̧tkowski · 2009
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Fixed-point property of random groups
H. Izeki, T. Kondo, and S. Nayatani · 2009
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