论文标题
高温渗透模型的连接衰减速率的存在和特性
Existence and properties of connections decay rate for high temperature percolation models
论文作者
论文摘要
我们考虑在高温假设下（连接概率的指数衰减和指数比弱混合），在$ \ mathbb {z}^d $上考虑通用有限范围渗透模型。我们证明，点对点连接的衰减速率在每个方向上都存在，并表明它自然地扩展到$ \ mathbb {r}^d $上的规范。该结果是获得对高温阶段的良好理解的基础输入，通常使用相关不平等（例如FKG）证明。目前的工作不使用这种模型特定属性。
We consider generic finite range percolation models on $\mathbb{Z}^d$ under a high temperature assumption (exponential decay of connection probabilities and exponential ratio weak mixing). We prove that the rate of decay of point-to-point connections exists in every directions and show that it naturally extends to a norm on $\mathbb{R}^d$. This result is the base input to obtain fine understanding of the high temperature phase and is usually proven using correlation inequalities (such as FKG). The present work makes no use of such model specific properties.
