Lipschitz embeddings of random fields
Probability Theory and Related Fields(2018)
摘要
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.
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