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29 March 2024
 
  » arxiv » math.PR/0204277

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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
AbstractA 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
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