Finitely dependent processes are finitary

Yinon Spinka

doi:10.1214/19-AOP1417

Finitely dependent processes are finitary

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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 Poincare Probab. Stat. 53 (2017) 753-765).

Original language	English
Pages (from-to)	2088-2177
Number of pages	90
Journal	Annals of Probability
Volume	48
Issue number	4
DOIs	https://doi.org/10.1214/19-AOP1417
State	Published - 1 Jul 2020
Externally published	Yes

Keywords

Amenable graph
Entropy
Finitary factor
Finitely dependent

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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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 Poincare Probab. Stat. 53 (2017) 753-765).",

keywords = "Amenable graph, Entropy, Finitary factor, Finitely dependent",

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PY - 2020/7/1

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N2 - 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 Poincare Probab. Stat. 53 (2017) 753-765).

AB - 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 Poincare Probab. Stat. 53 (2017) 753-765).

KW - Amenable graph

KW - Entropy

KW - Finitary factor

KW - Finitely dependent

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DO - 10.1214/19-AOP1417

M3 - مقالة

SN - 0091-1798

VL - 48

SP - 2088

EP - 2177

JO - Annals of Probability

JF - Annals of Probability

IS - 4

ER -

Finitely dependent processes are finitary

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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