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On the construction of the three-dimensional polymer measure


Bolthausen, E (1993). On the construction of the three-dimensional polymer measure. Probability Theory and Related Fields, 97(1-2):81-101.

Abstract

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.

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.

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20 citations in Web of Science®
16 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:coupling constant; three-dimensional polymer measure; small coupling parameter; Brydges-Fröhlich-Sokal construction
Language:English
Date:1993
Deposited On:20 May 2010 15:17
Last Modified:05 Apr 2016 13:28
Publisher:Springer
ISSN:0178-8051
Publisher DOI:https://doi.org/10.1007/BF01199313
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0794.60104

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