Lipschitz embeddings of random fields

• 成果类型: Article
• 署名作者: Basu, Riddhipratim; Sidoravicius, Vladas; Sly, Allan
• 署名单位: Tata Institute of Fundamental Research (TIFR); International Centre for Theoretical Sciences, Bengaluru; New York University; NYU Shanghai; Princeton University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0826-5
• 发表日期: 2018
• 页码: 1121-1179
• 关键词: dependent percolation; arbitrary words

摘要

We consider the problem of embedding one i.i.d. collection of Bernoulli random variables indexed by 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.