TY - JOUR
T1 - Lipschitz embeddings of random fields
AU - Basu, Riddhipratim
AU - Sidoravicius, Vladas
AU - Sly, Allan
N1 - Funding Information:
Acknowledgements This work was completed when R. B. was a graduate student at the Department of Statistics at UC Berkeley and the result in this paper appeared in Chapter 4 of his Ph.D. dissertation at UC Berkeley: Lipschitz Embeddings of Random Objects and Related Topics, 2015. R. B. gratefully acknowledges the support of UC Berkeley graduate fellowship. V. S. was supported by CNPq grant Bolsa de Produtividade. A. S. was supported by NSF grant DMS-1352013, and a Simons Investigator grant. We also thank an anonymous referee for many useful comments and suggestions that helped improve both the technical and editorial quality of the paper.
Funding Information:
This work was completed when R. B. was a graduate student at the Department of Statistics at UC Berkeley and the result in this paper appeared in Chapter 4 of his Ph.D. dissertation at UC Berkeley: Lipschitz Embeddings of Random Objects and Related Topics, 2015. R. B. gratefully acknowledges the support of UC Berkeley graduate fellowship. V. S. was supported by CNPq grant Bolsa de Produtividade. A. S. was supported by NSF grant DMS-1352013, and a Simons Investigator grant. We also thank an anonymous referee for many useful comments and suggestions that helped improve both the technical and editorial quality of the paper.
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/12/1
Y1 - 2018/12/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00440-017-0826-5
DO - 10.1007/s00440-017-0826-5
M3 - Article
AN - SCOPUS:85040678456
SN - 0178-8051
VL - 172
SP - 1121
EP - 1179
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
IS - 3-4
ER -