测量轮廓、聚合物或动物模型。概率方法
Measures on contour, polymer or animal models. A probabilistic approach
摘要：
我们提出了一种新的方法来研究的轮廓，聚合物或其他物体相互作用的某种排斥条件的合奏措施。为了具体起见，我们在这里对佩尔斯轮廓的情况展开。与现有的方法，这是基于集群扩展形式主义和/或复分析，我们的方法是严格的概率，因此可以应用，即使在没有分析性质。它涉及一个哈里斯图形结构的损失网络的措施的利益是不变的。该过程的存在和它的混合性质取决于一个双重（向后）导向的渗流过程，我们占主导地位的多型分支过程的无限集群的情况下。在该分支过程的亚临界区域内的方法产生：（一）指数收敛到平衡（=轮廓）措施，（二）标准聚类和有限效应性质的轮廓措施，（三）一个特别强大的形式的中心极限定理，和（四）泊松近似分布的轮廓在低温下。
英文摘要：
We present a new approach to study measures on ensembles of contours, polymers or other objects interacting by some sort of exclusion condition. For concreteness we develop it here for the case of Peierls contours. Unlike existing methods, which are based on cluster-expansion formalisms and/or complex analysis, our method is strictly probabilistic and hence can be applied even in the absence of analyticity properties. It involves a Harris graphical construction of a loss network for which the measure of interest is invariant. The existence of the process and its mixing properties depend on the absence of infinite clusters for a dual (backwards) oriented percolation process which we dominate by a multitype branching process. Within the region of subcriticality of this branching process the approach yields: (i) exponential convergence to the equilibrium (=contour) measures, (ii) standard clustering and finite-effect properties of the contour measure, (iii) a particularly strong form of the central limit theorem, and (iv) a Poisson approximation for the distribution of contours at low temperature.
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