论文标题
自由能，吉布斯的测量和Glauber动力学在树上最近的邻居相互作用
Free Energy, Gibbs Measures, and Glauber Dynamics for Nearest-neighbor Interactions on Trees
论文作者
论文摘要
我们将R. Holley的结果扩展到整数晶格之外，到包括自由组的大量组。特别是，当且仅当它是Glauber-Invariant的情况下，我们表明换档的度量是Gibbs。此外，在Glauber动力学下进化时，任何移位不变的度量都会微弱地收敛到吉布斯度量集。这些结果是使用新的自由能密度相对于同构近似的新自由能密度的概念。最小化自由能密度的任何措施都是吉布斯。
We extend results of R. Holley beyond the integer lattice to a large class of groups which includes free groups. In particular we show that a shift-invariant measure is Gibbs if and only if it is Glauber-invariant. Moreover, any shift-invariant measure converges weakly to the set of Gibbs measures when evolved under Glauber dynamics. These results are proven using a new notion of free energy density relative to a sofic approximation by homomorphisms. Any measure which minimizes free energy density is Gibbs.
