Approximating entropy for a class of ℤ<sup>2</sup>Markov random fields and pressure for a class of functions on ℤ<sup>2</sup>shifts of finite type
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Bibliographic record
Abstract
Abstract For a class of ℤ 2 Markov Random Fields (MRFs) μ , we show that the sequence of successive differences of entropies of induced MRFs on strips of height n converges exponentially fast (in n ) to the entropy of μ . These strip entropies can be computed explicitly when μ is a Gibbs state given by a nearest-neighbor interaction on a strongly irreducible nearest-neighbor ℤ 2 shift of finite type X . We state this result in terms of approximations to the (topological) pressures of certain functions on such an X , and we show that these pressures are computable if the values taken on by the functions are computable. Finally, we show that our results apply to the hard core model and Ising model for certain parameter values of the corresponding interactions, as well as to the topological entropy of certain nearest-neighbor ℤ 2 shifts of finite type, generalizing a result in [R. Pavlov. Approximating the hard square entropy constant with probabilistic methods. Ann. Probab. to appear].
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
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| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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