论文标题
共形措施和Dobrushin-Lanford-Ruelle方程
Conformal measures and the Dobrushin-Lanford-Ruelle equations
论文作者
论文摘要
我们证明了吉布斯对近改变的两个定义在可数群体上的等效性，即在多布鲁什林 - 兰福 - 荷兰（DLR）方程的意义上进行保形度量和吉布斯度量。我们相对于可测量的共生制定了经典DLR方程的更一般版本，当相互作用或潜力诱导Cocycle时，该方程将减小为经典方程，并表明满足这些方程的度量必须是完整的。为了确保这些结果与较早的工作的一致性，我们回顾了从电势构建相互作用的方法，反之亦然，从而使相互作用及其构成的潜力构成，反之亦然，会诱导相同的合子。
We demonstrate the equivalence of two definitions of a Gibbs measure on a subshift over a countable group, namely a conformal measure and a Gibbs measure in the sense of the Dobrushin-Lanford-Ruelle (DLR) equations. We formulate a more general version of the classical DLR equations with respect to a measurable cocycle, which reduce to the classical equations when the cocycle is induced by an interaction or a potential, and show that a measure satisfying these equations must be conformal. To ensure the consistency of these results with earlier work, we review methods of constructing an interaction from a potential and vice versa, such that the interaction and the potential constructed from it, or vice versa, induce the same cocycle.
