Gibbs States on Space-time

Gibbs states on path spaces of the form C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\left( {\mathbb{R},\mathbb{R}} \right)^{\mathbb{Z}^d }$$ \end{document} infinite stochastic differential equations of gradient type or as thermodynamic limits constructed with help of the method of cluster expansions.