Finitely dependent processes are finitary

Yinon Spinka

doi:10.1214/19-AOP1417

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Home > Journals > Ann. Probab. > Volume 48 > Issue 4 > Article

July 2020 Finitely dependent processes are finitary

Yinon Spinka

Ann. Probab. 48(4): 2088-2117 (July 2020). DOI: 10.1214/19-AOP1417

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Abstract

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).