NDLI: Lipschitz embeddings of random sequences

Content Provider	Springer Nature Link
Author	Basu, Riddhipratim Sly, Allan
Copyright Year	2013
Abstract	We develop a new multi-scale framework flexible enough to solve a number of problems involving embedding random sequences into random sequences. Grimmett et al. (Random Str Algorithm 37(1):85–99, 2010) asked whether there exists an increasing $$M$$ -Lipschitz embedding from one i.i.d. Bernoulli sequence into an independent copy with positive probability. We give a positive answer for large enough $$M$$ . A closely related problem is to show that two independent Poisson processes on $$\mathbb R $$ are roughly isometric (or quasi-isometric). Our approach also applies in this case answering a conjecture of Szegedy and of Peled (Ann Appl Probab 20:462–494, 2010). Our theorem also gives a new proof to Winkler’s compatible sequences problem. Our approach does not explicitly depend on the particular geometry of the problems and we believe it will be applicable to a range of multi-scale and random embedding problems.
Ending Page	775
Page Count	55
Starting Page	721
File Format	PDF
ISSN	01788051
e-ISSN	14322064
Journal	Probability Theory and Related Fields
Issue Number	3
Volume Number	159
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-07-28
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Rough isometry Compatible sequences Mathematical and Computational Biology Statistics for Business/Economics/Mathematical Finance/Insurance Theoretical, Mathematical and Computational Physics Operations Research/Decision Theory Percolation Interacting random processes; statistical mechanics type models; percolation theory Probability Theory and Stochastic Processes Lipschitz embedding Quantitative Finance
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Analysis Statistics, Probability and Uncertainty

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