# Finitely dependent processes are finitary

## TL;DR

The paper proves that finitely dependent invariant processes on transitive amenable graphs can be represented as finitary factors of i.i.d. processes, with entropy arbitrarily close under certain geometric conditions.

## Contribution

It establishes a new representation theorem linking finitely dependent processes to i.i.d. processes on specific graphs, answering a question of Holroyd.

## Key findings

- Finitely dependent invariant processes are finitary factors of i.i.d. processes.
- Under certain geometric conditions, the entropy of the i.i.d. process can be made arbitrarily close.
- Provides an affirmative answer to Holroyd's question.

## 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.