On the construction of the three dimensional polymer measure
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- Bolthausen, E. Probab. Th. Rel. Fields (1993) 97: 81. doi:10.1007/BF01199313
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The three dimensional polymer measure was first constructed by Westwater in 1980 with a very complicated proof. We give an alternative construction for small coupling parameter which is based on the approach by Brydges-Fröhlich-Sokal in quantum field theory and Bovier-Felder-Fröhlich, 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.