{"id":340271,"date":"2016-12-21T16:10:20","date_gmt":"2016-12-22T00:10:20","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-research-item&p=340271"},"modified":"2018-10-16T21:22:15","modified_gmt":"2018-10-17T04:22:15","slug":"lipschitz-percolation","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/lipschitz-percolation\/","title":{"rendered":"Lipschitz Percolation"},"content":{"rendered":"

We prove the existence of a (random) Lipschitz function F : Zd\u22121<\/sup><\/em> \u2192 Z+<\/sup> such that, for every x \u2208 Zd\u22121<\/sup>,<\/em> the site (x<\/em>, F(x<\/em>)) is open in a site percolation process on Zd<\/sup><\/em> . The Lipschitz constant may be taken to be 1 when the parameter p of the percolation model is sufficiently close to 1. Alexander Holroyd<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

We prove the existence of a (random) Lipschitz function F : Zd\u22121 \u2192 Z+ such that, for every x \u2208 Zd\u22121, the site (x, F(x)) is open in a site percolation process on Zd . The Lipschitz constant may be taken to be 1 when the parameter p of the percolation model is sufficiently close […]<\/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":"Institute of Mathematical Statistics","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"Electronic Communications in 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