The wreath product of Z with Z has Hilbert compression exponent 2/3

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dc.creatorAustin, Tim
dc.creatorNaor, Assaf
dc.creatorPeres, Yuval
dc.date2007-06-13
dc.date2007-08-13
dc.date.accessioned2026-07-07T08:23:01Z
dc.date.available2026-07-07T08:23:01Z
dc.descriptionLet 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 $α\ge 0$ such that there exists a Lipschitz mapping $f:G\to L_2$ and a constant $c>0$ such that for all $x,y\in G$ we have $\|f(x)-f(y)\|_2\ge cd(x,y)^α.$ In \cite{AGS06} it was shown that the Hilbert compression exponent of the wreath product $\Z\bwr \Z $ is at most $\frac34$, and in \cite{NP07} was proved that this exponent is at least $\frac23$. Here we show that $\frac23$ is the correct value. Our proof is based on an application of K. Ball's notion of Markov type.
dc.descriptionRemoved a reference to the lower bound of 2/3 for the Hilbert compression of Z wreath Z in math/0603138 since the proof is incorrect; added a reference which contains a correct proof (the results of this paper remain unchanged). Added Remark 2.2 which shows why Z wreath Z has Hilbert compression exponent at least 2/3
dc.identifierhttps://arxiv.org/abs/0706.1943
dc.identifierhttp://arxiv.org/abs/0706.1943
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/135845
dc.subjectMetric Geometry
dc.subjectFunctional Analysis
dc.subjectGroup Theory
dc.titleThe wreath product of Z with Z has Hilbert compression exponent 2/3
dc.typetext

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