Mallows Permutations and Finite Dependence

Alexander Holroyd, Tom Hutchcroft, Avi Levy

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

We use the Mallows permutation model to construct a new family of stationary finitely dependent proper colorings of the integers. We prove that these colorings can be expressed as finitary factors of i.i.d. processes with finite mean coding radii. They are the first colorings known to have these properties. Moreover, we prove that the coding radii have exponential tails, and that the colorings can also be expressed as functions of countable-state Markov chains. We deduce analogous existence statements concerning shifts of finite type and higher-dimensional colorings.
Original languageEnglish
Pages (from-to)343-379
Number of pages37
JournalAnnals of Probability
Volume48
Issue number1
Early online date25 Mar 2020
DOIs
Publication statusE-pub ahead of print - 25 Mar 2020

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