Lp compression, traveling salesmen, and stable walks

Assaf Naor, Yuval Peres

Research output: Contribution to journalArticlepeer-review

Abstract

We show that if H is a group of polynomial growth whose growth rate is at least quadratic, then the Lp compression of the wreath product Z{double-struck} {wreath product} H equals max. We also show that the Lp compression of Z{double-struck} {wreath product} Z{double-struck} equals max and that the Lp compression of(Z{double-struck} {wreath product} Z{double-struck})0 (the zero section of Z{double-struck} {wreath product} Z{double-struck}, equipped with the metric induced from Z{double-struck} {wreath product} Z) equals max. The fact that the Hilbert compression exponent of Z{double-struck} {wreath product} Z{double-struck} equals 2/3 while the Hilbert compression exponent of (Z{double-struck} {wreath product} Z{double-struck})0 equals 3/4 is used to show that there exists a Lipschitz function f : (Z{double-struck} {wreath product} Z{double-struck})0 → L2 which cannot be extended to a Lipschitz function defined on all of Z{double-struck} {wreath product} Z{double-struck}.

Original languageEnglish (US)
Pages (from-to)53-108
Number of pages56
JournalDuke Mathematical Journal
Volume157
Issue number1
DOIs
StatePublished - Mar 15 2011

ASJC Scopus subject areas

  • Mathematics(all)

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