## Electronic Journal of Probability

### Finitary coding for the sub-critical Ising model with finite expected coding volume

Yinon Spinka

#### Abstract

It has been shown by van den Berg and Steif [5] that the sub-critical Ising model on $\mathbb{Z} ^{d}$ is a finitary factor of a finite-valued i.i.d. process. We strengthen this by showing that the factor map can be made to have finite expected coding volume (in fact, stretched-exponential tails), answering a question of van den Berg and Steif. The result holds at any temperature above the critical temperature. An analogous result holds for Markov random fields satisfying a high-noise assumption and for proper colorings with a large number of colors.

#### Article information

Source
Electron. J. Probab., Volume 25 (2020), paper no. 8, 27 pp.

Dates
Accepted: 17 January 2020
First available in Project Euclid: 29 January 2020

https://projecteuclid.org/euclid.ejp/1580267008

Digital Object Identifier
doi:10.1214/20-EJP420

#### Citation

Spinka, Yinon. Finitary coding for the sub-critical Ising model with finite expected coding volume. Electron. J. Probab. 25 (2020), paper no. 8, 27 pp. doi:10.1214/20-EJP420. https://projecteuclid.org/euclid.ejp/1580267008

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