Finitely dependent processes are finitary
Probability
2020-01-22 v2
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.
Cite
@article{arxiv.1901.00123,
title = {Finitely dependent processes are finitary},
author = {Yinon Spinka},
journal= {arXiv preprint arXiv:1901.00123},
year = {2020}
}
Comments
28 pages, 1 figure; Minor improvements to text, added an open question