论文标题
与Gibbs措施相关的无限尺寸操作员的固定点
Fixed points of an infinite dimensional operator related to Gibbs measures
论文作者
论文摘要
我们描述了与硬核（HC）模型相关的无限尺寸非线性运算符的固定点，该模型具有可数集的Cayley树上旋转值的$ \ Mathbb {n} $。该运算符由一组可数参数集$λ_{i}> 0 $，$ a_ {ij} \ in \ {0,1 \} $，$ i，$ i，j \ in \ mathbb {n} $。我们在这些参数上找到了足够的条件，在这些参数下，操作员具有唯一的固定点。如果不满足此条件，我们表明操作员最多可能具有五个固定点。另外，我们证明每个固定点都会生成一个可正常的边界定律，因此定义了给定HC模型的Gibbs度量。
We describe fixed points of an infinite dimensional non-linear operator related to a hard core (HC) model with a countable set $\mathbb{N}$ of spin values on the Cayley tree. This operator is defined by a countable set of parameters $λ_{i}>0$, $a_{ij}\in \{0,1\}$, $ i,j \in \mathbb{N}$. We find a sufficient condition on these parameters under which the operator has unique fixed point. When this condition is not satisfied then we show that the operator may have up to five fixed points. Also, we prove that every fixed point generates a normalisable boundary law and therefore defines a Gibbs measure for the given HC-model.
