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math.MG2007★ 22 cited
The wreath product of Z with Z has Hilbert compression exponent 2/3
Tim Austin, Assaf Naor, Yuval Peres
Let G be a finitely generated group, equipped with the word metric d associated with some finite set of generators. The Hilbert compression exponent of G is the supremum over all $…
math.MG2007★ 4 cited
The Euclidean distortion of the lamplighter group
Tim Austin, Assaf Naor, Alain Valette
We show that the cyclic lamplighter group $C_2 \bwr C_n$ embeds into Hilbert space with distortion . This matches the lower bound proved by Lee, Naor and Pe…