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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty