Electronic Journal of Probability

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

Yinon Spinka

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1580267008

Digital Object Identifier
doi:10.1214/20-EJP420

Subjects
Primary: 28D99: None of the above, but in this section 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Secondary: 82B26: Phase transitions (general) 37A60: Dynamical systems in statistical mechanics [See also 82Cxx]

Keywords
Ising model finitary coding finite expected coding volume

Rights
Creative Commons Attribution 4.0 International License.

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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