On the scaling limit of planar self-avoiding walk

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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.

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Probability, Mathematical Physics, 60K35, 82B41

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http://salesiana.dossiersoluciones.com/handle/123456789/95650

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0204277
 http://arxiv.org/abs/math/0204277
 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

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arXiv