Lipschitz embeddings of random fields

Riddhipratim Basu; Vladas Sidoravicius; Allan Sly

doi:10.1007/s00440-017-0826-5

Lipschitz embeddings of random fields

Riddhipratim Basu
, Vladas Sidoravicius
, Allan Sly

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We consider the problem of embedding one i.i.d. collection of Bernoulli random variables indexed by Z^d 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 language	English (US)
Pages (from-to)	1121-1179
Number of pages	59
Journal	Probability Theory and Related Fields
Volume	172
Issue number	3-4
DOIs	https://doi.org/10.1007/s00440-017-0826-5
State	Published - Dec 1 2018

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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Cite this

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Lipschitz embeddings of random fields

Abstract

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