On the scaling limit of planar self-avoiding walk

Details On the scaling limit of planar self-avoiding walk On the scaling limit of planar self-avoiding walk

2002-04-23

arxiv.org/abs/math/0204277v2

Fractal geometry and applications: a jubilee of Beno\^it Mandelbrot, Part 2, 339--364, Proc. Sympos. Pure Math., 72, Part 2, A

Mathematics

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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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