L p compression, traveling salesmen, and stable walks

Assaf Naor, Yuval Peres

Research output: Contribution to journalArticle

Abstract

We show that if H is a group of polynomial growth whose growth rate is at least quadratic, then the L p compression of the wreath product Z{double-struck} {wreath product} H equals max. We also show that the L p compression of Z{double-struck} {wreath product} Z{double-struck} equals max and that the L p 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 → L 2 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

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Travelling salesman
Wreath Product
Walk
Compression
Lipschitz Function
Hilbert
Exponent
Polynomial Growth

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

L p compression, traveling salesmen, and stable walks. / Naor, Assaf; Peres, Yuval.

In: Duke Mathematical Journal, Vol. 157, No. 1, 15.03.2011, p. 53-108.

Research output: Contribution to journalArticle

Naor, Assaf ; Peres, Yuval. / L p compression, traveling salesmen, and stable walks. In: Duke Mathematical Journal. 2011 ; Vol. 157, No. 1. pp. 53-108.
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