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摘要翻译：
引入二维离散随机场P沿曲线c的表面级比熵h_c(P)的概念，作为c爆破的格子近似的重标熵的极限。通过证明一个相应的Shannon-McMillan定理来说明存在性。我们得到了h_c(P)的一个表示，它是沿着C的切线的特定熵的混合物。作为应用，利用沿曲线的比熵，从相变区的遍历行为出发，对吸引吉布斯测度经验场的大偏差的Foellmer和ORT下界进行了精化。
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英文标题：
《Shannon-McMillan theorems for discrete random fields along curves and
lower bounds for surface-order large deviations》
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作者：
Julia Brettschneider
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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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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PDF链接：
https://arxiv.org/pdf/709.2662
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