Finitary coding for the one-dimensional ${T,T^{-1}}$ process with drift

Michael Keane; Jeffrey E. Steif

doi:10.1214/aop/1068646374

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

Published: October 2003

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