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• W1972474077 abstract "We show that the cyclic lamplighter group C 2 ≀ C n embeds into Hilbert space with distortion $mathrm{O}(sqrt{log n})$ . This matches the lower bound proved by Lee et al. (Geom. Funct. Anal., 2009), answering a question posed in that paper. Thus, the Euclidean distortion of C 2 ≀ C n is $varTheta(sqrt{log n})$ . Our embedding is constructed explicitly in terms of the irreducible representations of the group. Since the optimal Euclidean embedding of a finite group can always be chosen to be equivariant, as shown by Aharoni et al. (Isr. J. Math. 52(3):251–265, 1985) and by Gromov (see de Cornulier et. al. in Geom. Funct. Anal., 2009), such representation-theoretic considerations suggest a general tool for obtaining upper and lower bounds on Euclidean embeddings of finite groups." @default.
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• W1972474077 date "2009-04-17" @default.
• W1972474077 modified "2023-09-27" @default.
• W1972474077 title "The Euclidean Distortion of the Lamplighter Group" @default.
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• W1972474077 doi "https://doi.org/10.1007/s00454-009-9162-6" @default.
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