Probability Theory and Related Fields

, Volume 97, Issue 1, pp 81-101

First online:

On the construction of the three dimensional polymer measure

  • Erwin BolthausenAffiliated withInstitut fúr Angewandte Mathematik, Universitát Zúrich

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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.