Pacific Northwest Probability Seminar: An Analysis of Spatial Mixing

  • Persi Diaconis  | Stanford University

In joint work with Soumik Pal, we study natural mixing processes where cards (or dominoes or mahjong tiles) are ‘smushed’ around on a table with two hands. How long should mixing continue. If things are not well mixed, what patterns remain? We study this in practice (!): experiments indicate that about 30 seconds of smushing suffice to mix 52 cards. We also study it in theory introducing a variety of models which permit analysis. Part of the analysis passes to a reflecting, jump- diffusion limit and uses this and a novel ‘shadow coupling’ to give reasonably precise bounds on the mixing time.

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