论文标题
吉布斯字段的独特性，在无界度图上具有无界随机相互作用
Uniqueness of Gibbs fields with unbounded random interactions on unbounded degree graphs
论文作者
论文摘要
研究了带有连续旋转的吉布斯字段，其基础图可以是无限的顶点程度，并且自旋旋转对相互作用势是随机且无限的。事实证明，在以下条件下证明了这种领域的高温唯一性：（a）顶点程度具有脾气暴躁的生长，即以某种方式控制； （b）交互潜力$ w_ {xy} $使$ \ | w_ {xy} \ | = \ | = \ sup_ {σ，σ，σ'} | w_ {xy}（xy}（σ，σ'）| $是独立的（对于不同的边缘$ \ langle x，y \ y \ rangle $），并识别分布，并构成分布。
Gibbs fields with continuous spins are studied, the underlying graphs of which can be of unbounded vertex degree and the spin-spin pair interaction potentials are random and unbounded. A high-temperature uniqueness of such fields is proved to hold under the following conditions: (a) the vertex degree is of tempered growth, i.e., controlled in a certain way; (b) the interaction potentials $W_{xy}$ are such that $\|W_{xy}\|=\sup_{σ,σ'} |W_{xy}(σ, σ')|$ are independent (for different edges $\langle x, y \rangle$), identically distributed and exponentially integrable random variables.
