{"id":357785,"date":"2017-01-25T13:48:49","date_gmt":"2017-01-25T21:48:49","guid":{"rendered":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/?post_type=msr-research-item&p=357785"},"modified":"2018-10-16T20:00:58","modified_gmt":"2018-10-17T03:00:58","slug":"lp-compression-traveling-salesmen-stable-walks","status":"publish","type":"msr-research-item","link":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/publication\/lp-compression-traveling-salesmen-stable-walks\/","title":{"rendered":"LP Compression, Traveling Salesmen, And Stable Walks"},"content":{"rendered":"

We show that if H<\/span><\/span><\/span><\/span> is a group of polynomial growth whose growth rate is at least quadratic then the L<\/span>p<\/span><\/span><\/span><\/span><\/span> compression of the wreath product $\\Z\\bwr H$<\/span><\/span><\/span> equals max<\/span>1<\/span>p<\/span><\/span>,<\/span>1<\/span>\/<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>. We also show that the L<\/span>p<\/span><\/span><\/span><\/span><\/span>compression of $\\Z\\bwr \\Z$<\/span><\/span><\/span> equals max<\/span>p<\/span>2<\/span>p<\/span>\u2212<\/span>1<\/span><\/span><\/span>,<\/span>2<\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span> and the L<\/span>p<\/span><\/span><\/span><\/span><\/span> compression of $(\\Z\\bwr\\Z)_0$<\/span><\/span><\/span> (the zero section of $\\Z\\bwr \\Z$<\/span><\/span><\/span>, equipped with the metric induced from $\\Z\\bwr \\Z$<\/span><\/span><\/span>) equals max<\/span>p<\/span>+<\/span>1<\/span><\/span>2<\/span>p<\/span><\/span><\/span>,<\/span>3<\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/span>. The fact that the Hilbert compression exponent of $\\Z\\bwr\\Z$<\/span><\/span><\/span> equals 2<\/span>3<\/span><\/span><\/span><\/span><\/span> while the Hilbert compression exponent of $(\\Z\\bwr\\Z)_0$<\/span><\/span><\/span> equals 3<\/span>4<\/span><\/span><\/span><\/span><\/span> is used to show that there exists a Lipschitz function $f:(\\Z\\bwr\\Z)_0\\to L_2$<\/span><\/span><\/span> which cannot be extended to a Lipschitz function defined on all of $\\Z\\bwr \\Z$<\/span><\/span><\/span>.<\/p>\n","protected":false},"excerpt":{"rendered":"

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 $\\Z\\bwr H$ equals max1p,1\/2. We also show that the Lpcompression of $\\Z\\bwr \\Z$ equals maxp2p\u22121,23 and the Lp compression of $(\\Z\\bwr\\Z)_0$ (the zero section of $\\Z\\bwr \\Z$, equipped with […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Duke University Press","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"Duke Mathematical 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