Lipschitz embeddings of random fields

Riddhipratim Basu, Vladas Sidoravicius, Allan Sly

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the problem of embedding one i.i.d. collection of Bernoulli random variables indexed by Zd into an independent copy in an injective M-Lipschitz manner. For the case d= 1 , it was shown in Basu and Sly (Probab Theory Relat Fields 159:721–775, 2014) to be possible almost surely for sufficiently large M. In this paper we provide a multi-scale argument extending this result to higher dimensions.

Original languageEnglish (US)
Pages (from-to)1121-1179
Number of pages59
JournalProbability Theory and Related Fields
Volume172
Issue number3-4
DOIs
StatePublished - Dec 1 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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