## Finitely dependent processes are finitary.(English)Zbl 1453.60150

Summary: 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 A. E. Holroyd [Ann. Inst. Henri Poincaré, Probab. Stat. 53, No. 2, 753–765 (2017; Zbl 1370.60061)].

### MSC:

 60J99 Markov processes 60G10 Stationary stochastic processes 28D99 Measure-theoretic ergodic theory 37A35 Entropy and other invariants, isomorphism, classification in ergodic theory

### Keywords:

finitary factor; finitely dependent; entropy; amenable graph

Zbl 1370.60061
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### References:

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