Square summability of variations of g-functions and uniqueness of g-measures
Square summability of variations of g-functions and uniqueness of g-measures
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DOI：
10.4310/mrl.2003.v10.n5.a3
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发表时间：
2003
影响因子：
1
通讯作者：
Anders Johansson;Anders Öberg
中科院分区：
文献类型：
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作者：
Anders Johansson;Anders Öberg
证明了满足变差二次可和性的g-函数的g-测度的唯一性。我们的结果是在相反的情况下，\例如，一维伊辛模型与长程相互作用，因为$\ell_1 $-summability的变化是必需的一般潜力。我们用一些例子来说明这种差异。为了证明我们的主要结果，我们使用一个产品鞅的论点。我们还给出了条件的唯一性的一般$G $措施，\即情况下，一般的潜力，根据我们的调查的概率情况下，涉及$G$-功能。
We prove uniqueness of $g$-measures for $g$-functions satisfying quadratic summability of variations. Our result is in contrast to the situation of, \eg, the one-dimensional Ising model with long-range interactions, since $\ell_1$-summability of variations is required for general potentials. We illustrate this difference with some examples. To prove our main result we use a product martingale argument. We also give conditions for uniqueness of general $G$-measures, \ie, the case for general potentials, based on our investigation of the probabilistic case involving $g$-functions.