# Lipschitz embeddings of random fields

Probability Theory and Related Fields, pp. 1-59, 2018.

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Abstract:

We consider the problem of embedding one i.i.d. collection of Bernoulli random variables indexed by \({\mathbb {Z}}^d\) 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 thi...More

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