On the construction of the three dimensional polymer measure (Q1326242)

The three-dimensional polymer measure was first constructed by \textit{J. Westwater} [Commun. Math. Phys. 72, 131-174 (1980; Zbl 0431.60100)] with a very complicated proof. We give an alternative construction for small coupling parameter which is based on the approach by \textit{D. C. Brydges}, \textit{J. Fröhlich} and \textit{A. Sokal} [ibid. 91, 141 (1983)] in quantum field theory and \textit{A. Bovier}, \textit{G. Felder} and \textit{J. Fröhlich} [Nucl. Phys., Ser. B. 230, 119-147 (1984)] using skeleton inequalities. The main new features are the proof of convergence which had been open in the Brydges-Fröhlich-Sokal construction, and the construction of the measure on the space of paths with fixed time length.