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We show that the cyclic lamplighter group $C_2 \bwr C_n$ embeds into Hilbert space with distortion ${\rm O}(\sqrt{\log n})$.
Uniform embeddings of metric spaces and of Banach spaces into Hilbert spaces
I. Aharoni, B. Maurey, and B. S. Mityagin · 1985
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The metrical interpretation of superreflexivity in Banach spaces
J. Bourgain · 1986
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Representation theory
W. Fulton and J. Harris · 1991
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Markov chains, Riesz transforms and Lipschitz maps
K. Ball · 1992
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Random Cayley graphs and expanders
N. Alon and Y. Roichman · 1994
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Random walks on the lamplighter group
R. Lyons, R. Pemantle, and Y. Peres · 1996
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Euclidean distortion and the Sparsest Cut
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Isometric group actions on Hilbert spaces: growth of cocycles
Y. de Cornulier, R. Tessera, and A. Valette
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Trees and Markov convexity
J. R. Lee, A. Naor, and Y. Peres
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Integrality gap for cut problems and embeddability of negative type metrics into l1
S. Khot and N. K. Vishnoi · 2005
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Differentiating maps into L 1 {L}^{1} and the geometry of BV functions
J. Cheeger and B. Kleiner · 2006
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Nonembeddability theorems via Fourier analysis
S. Khot and A. Naor · 2006
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L p {L}_{p} metrics on the Heisenberg group and the Goemans-Linial conjecture
J. R. Lee and A. Naor · 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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