Functional integral representations for self-avoiding walk
David C. Brydges, John Z. Imbrie, and Gordon Slade
Source: Probab. Surveys Volume 6
(2009), 34-61.
Abstract
We give a survey and unified treatment of functional integral representations for both simple random walk and some self-avoiding walk models, including models with strict self-avoidance, with weak self-avoidance, and a model of walks and loops. Our representation for the strictly self-avoiding walk is new. The representations have recently been used as the point of departure for rigorous renormalization group analyses of self-avoiding walk models in dimension 4. For the models without loops, the integral representations involve fermions, and we also provide an introduction to fermionic integrals. The fermionic integrals are in terms of anticommuting Grassmann variables, which can be conveniently interpreted as differential forms.
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Permanent link to this document: http://projecteuclid.org/euclid.ps/1249996530
Digital Object Identifier: doi:10.1214/09-PS152
Mathematical Reviews number (MathSciNet): MR2525670
Zentralblatt MATH identifier: 05728612
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