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 language | English (US) |
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Pages (from-to) | 1121-1179 |
Number of pages | 59 |
Journal | Probability Theory and Related Fields |
Volume | 172 |
Issue number | 3-4 |
DOIs | |
State | Published - Dec 1 2018 |
All Science Journal Classification (ASJC) codes
- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty