曲线离散随机场的Shannon-McMillan定理和曲面阶大偏差的下界
Shannon-McMillan theorems for discrete random fields along curves and lower bounds for surface-order large deviations
摘要：
引入了二维离散随机场P沿曲线c的表面阶比熵h_c（P）的概念，作为沿c的爆破的格点逼近的重标熵的极限。证明了相应的Shannon-McMillan定理。我们得到了h_c（P）沿c的切线的混合熵表示。作为一个应用，特定的熵沿曲线被用来完善Foellmer和Ort的下界的大偏差的经验领域的吸引力吉布斯措施从其遍历行为的相变制度。
英文摘要：
The notion of a surface-order specific entropy h_c(P) of a two-dimensional discrete random field P along a curve c is introduced as the limit of rescaled entropies along lattice approximations of the blowups of c. Existence is shown by proving a corresponding Shannon-McMillan theorem. We obtain a representation of h_c(P) as a mixture of specific entropies along the tangent lines of c. As an application, the specific entropy along curves is used to refine Foellmer and Ort's lower bound for the large deviations of the empirical field of an attractive Gibbs measure from its ergodic behavior in the phase-transition regime.
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