2012/04/13 by Riddhipratim Basu, Basu, Riddhipratim, Allan Sly +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #Probability (math.PR) #math.CO #math.PR
paper · pdf · doi:10.48550/arxiv.1204.2931
46 pages, 3 figures added
openalex publication_date 2012/04/13 · arxiv created 2012/04/19 · arxiv updated 2012/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a new multi-scale framework flexible enough to solve a number of problems involving embedding random sequences into random sequences. Grimmett, Liggett and Richthammer asked whether there exists an increasing M-Lipschitz embedding from one i.i.d. Bernoulli sequences 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 R are roughly isometric (or quasi-isometric). Our approach also applies in this case answering a conjecture of Szegedy and of Peled. Our theorem also gives a new proof to Winkler's compatible sequences problem.