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October 2003 Finitary coding for the one-dimensional ${T,T^{-1}}$ process with drift
Michael Keane, Jeffrey E. Steif
Ann. Probab. 31(4): 1979-1985 (October 2003). DOI: 10.1214/aop/1068646374

Abstract

We show that there is a finitary isomorphism from a finite state independent and identically distributed (i.i.d.) process to the $T,T^{-1}$ process associated to one-dimensional random walk with positive drift. This contrasts with the situation for simple symmetric random walk in any dimension, where it cannot be a finitary factor of any i.i.d. process, including in $d\ge 5$, where it becomes weak Bernoulli.

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Michael Keane. Jeffrey E. Steif. "Finitary coding for the one-dimensional ${T,T^{-1}}$ process with drift." Ann. Probab. 31 (4) 1979 - 1985, October 2003. https://doi.org/10.1214/aop/1068646374

Information

Published: October 2003
First available in Project Euclid: 12 November 2003

zbMATH: 1053.60035
MathSciNet: MR2016608
Digital Object Identifier: 10.1214/aop/1068646374

Subjects:
Primary: 28D99, 37A35, 37A50, 60G10

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 4 • October 2003
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