Open Access
July 2020 Finitely dependent processes are finitary
Yinon Spinka
Ann. Probab. 48(4): 2088-2117 (July 2020). DOI: 10.1214/19-AOP1417


We show that any finitely dependent invariant process on a transitive amenable graph is a finitary factor of an i.i.d. process. With an additional assumption on the geometry of the graph, namely that no two balls with different centers are identical, we further show that the i.i.d. process may be taken to have entropy arbitrarily close to that of the finitely dependent process. As an application, we give an affirmative answer to a question of Holroyd (Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017) 753–765).


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Yinon Spinka. "Finitely dependent processes are finitary." Ann. Probab. 48 (4) 2088 - 2117, July 2020.


Received: 1 March 2019; Published: July 2020
First available in Project Euclid: 20 July 2020

zbMATH: 07224969
MathSciNet: MR4124534
Digital Object Identifier: 10.1214/19-AOP1417

Primary: 60G10 , 60J99
Secondary: 28D99 , 37A35

Keywords: amenable graph , Entropy , Finitary factor , finitely dependent

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 4 • July 2020
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