Dimensions
DimensionsBasu, Riddhipratim ; Sidoravicius, Vladas ; Sly, Allan (2018) Lipschitz embeddings of random fields Probability Theory and Related Fields, 172 . pp. 1121-1179. ISSN 0178-8051
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Official URL: https://doi.org/10.1007/s00440-017-0826-5
Related URL: http://dx.doi.org/10.1007/s00440-017-0826-5
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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Springer-Verlag. |
| ID Code: | 142053 |
| Deposited On: | 30 Dec 2025 14:35 |
| Last Modified: | 30 Dec 2025 14:35 |
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