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Article overview
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On the scaling limit of planar self-avoiding walk | Gregory F. Lawler
; Oded Schramm
; Wendelin Werner
; | Date: |
23 Apr 2002 | Journal: | Fractal geometry and applications: a jubilee of Benoît Mandelbrot, Part 2, 339--364, Proc. Sympos. Pure Math., 72, Part 2, Amer. Math. Soc., Providence, RI, 2004 | Subject: | Probability; Mathematical Physics MSC-class: 60K35, 82B41 | math.PR math-ph math.MP | Abstract: | A planar self-avoiding walk (SAW) is a nearest neighbor random walk path in the square lattice with no self-intersection. A planar self-avoiding polygon (SAP) is a loop with no self-intersection. In this paper we present conjectures for the scaling limit of the uniform measures on these objects. The conjectures are based on recent results on the stochastic Loewner evolution and non-disconnecting Brownian motions. New heuristic derivations are given for the critical exponents for SAWs and SAPs. | Source: | arXiv, math.PR/0204277 | Services: | Forum | Review | PDF | Favorites |
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