ON THE CONSTRUCTION OF THE 3-DIMENSIONAL POLYMER MEASURE

The three dimensional polymer measure was first constructed by West-water in 1980 with a very complicated proof We give an alternative construction for small coupling parameter which is based on the approach by Brydges-Frohlich-Sokal in quantum field theory and Bovier-Felder-Frohlich, using skeleton inequalities. The main new features are the proof of convergence which had been open in the Brydges-Frohlich-Sokal construction, and the construction of the measure on the space of paths with fixed time length.