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January 2020 Mallows permutations and finite dependence
Alexander E. Holroyd, Tom Hutchcroft, Avi Levy
Ann. Probab. 48(1): 343-379 (January 2020). DOI: 10.1214/19-AOP1363

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.

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Alexander E. Holroyd. Tom Hutchcroft. Avi Levy. "Mallows permutations and finite dependence." Ann. Probab. 48 (1) 343 - 379, January 2020. https://doi.org/10.1214/19-AOP1363

Information

Received: 1 June 2017; Revised: 1 January 2019; Published: January 2020
First available in Project Euclid: 25 March 2020

zbMATH: 07206761
MathSciNet: MR4079439
Digital Object Identifier: 10.1214/19-AOP1363

Subjects:
Primary: 60G10
Secondary: 05A05, 05C15

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • January 2020
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