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2020 Finitary coding for the sub-critical Ising model with finite expected coding volume
Yinon Spinka
Electron. J. Probab. 25(none): 1-27 (2020). DOI: 10.1214/20-EJP420

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.

Citation

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Yinon Spinka. "Finitary coding for the sub-critical Ising model with finite expected coding volume." Electron. J. Probab. 25 1 - 27, 2020. https://doi.org/10.1214/20-EJP420

Information

Received: 6 November 2018; Accepted: 17 January 2020; Published: 2020
First available in Project Euclid: 29 January 2020

zbMATH: 1441.60088
MathSciNet: MR4059186
Digital Object Identifier: 10.1214/20-EJP420

Subjects:
Primary: 28D99, 60K35, 82B20
Secondary: 37A60, 82B26

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