论文标题
晶格系统中的高斯浓度和平衡状态的独特性
Gaussian concentration and uniqueness of equilibrium states in lattice systems
论文作者
论文摘要
我们考虑配置空间上的平衡状态（即，换档gibbs测量）$ s^{\ mathbb {z}^d} $其中$ d \ geq 1 $和$ s $是有限的集合。我们证明，如果用于移位不变的均匀总结电势的平衡状态满足高斯浓度的结合，则它是唯一的。同等地，如果存在一些均衡状态，则没有一个能够满足这种结合的能力。
We consider equilibrium states (that is, shift-invariant Gibbs measures) on the configuration space $S^{\mathbb{Z}^d}$ where $d\geq 1$ and $S$ is a finite set. We prove that if an equilibrium state for a shift-invariant uniformly summable potential satisfies a Gaussian concentration bound, then it is unique. Equivalently, if there exist several equilibrium states for a potential, none of them can satisfy such a bound.
