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Lipschitz embeddings of random sequences.

Mathematical Physics & Probability

Speaker: Riddhipratim Basu, UC Berkeley
Location: 1147 MSB
Start time: Wed, Oct 17 2012, 4:10PM

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 $\mathbb{R}$ 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. This is joint work with Allan Sly.