On the construction of the three dimensional polymer measure
type: Item
instance of: scholarly article
title: On the construction of the three dimensional polymer measure
zbMATH Open document ID: 0794.60104
DOI: 10.1007/BF01199313
author: Erwin Bolthausen
publication date: 1994-08-15T00:00:00Z
review text: 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.
reviewed by: Erwin Bolthausen
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82D60
zbMATH DE Number: 568981
zbMATH Keywords: coupling constant
zbMATH Keywords: three-dimensional polymer measure
zbMATH Keywords: small coupling parameter
zbMATH Keywords: Brydges-Fröhlich-Sokal construction
MaRDI profile type: Publication
cites work: Regularized self-intersection local times of planar Brownian motion
cites work: Q4725438
cites work: A local time approach to the self-intersections of Brownian paths in space
cites work: On Edwards' model for long polymer chains
cites work: On Edwards' model for polymer chains. III. Borel summability
cites work: Q3676928
cites work: The intersection local time of the Westwater process
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 568981