Finitary coding for the sub-critical Ising model with finite expected coding volume
| Autor: | Yinon Spinka |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
finite expected coding volume 82B20 01 natural sciences 010104 statistics & probability Ising model FOS: Mathematics Sub critical Finitary 0101 mathematics Mathematics Discrete mathematics Random field Markov chain Probability (math.PR) 010102 general mathematics finitary coding 60K35 28D99 60K35 82B20 82B26 37A60 82B26 37A60 Statistics Probability and Uncertainty 28D99 Mathematics - Probability Coding (social sciences) |
| Zdroj: | Electronic Journal of Probability Electron. J. Probab. |
| ISSN: | 1083-6489 |
| DOI: | 10.1214/20-ejp420 |
| Popis: | It has been shown by van den Berg and Steif 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. Comment: 24 pages, 1 figure. Renumbered theorems, minor improvements to text |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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