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On the scaling limit of planar self-avoiding walk

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arxiv math/0204277 v2 pith:KI7ZN5RT submitted 2002-04-23 math.PR math-phmath.MP

Gregory F. Lawler , Oded Schramm , Wendelin Werner This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords planarself-avoidingwalkconjectureslimitscalingself-intersectionbrownian
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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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Cited by 1 Pith paper

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  1. Complexity and Geometry of Sampling Connected Graph Partitions

    cs.CC 2019-08 accept novelty 7.0 of 10

    Uniform and balanced sampling of connected planar graph partitions is hard unless RP=NP, the flip walk mixes exponentially slowly on explicit triangulation families, and tractable cases include series-parallel and bou...

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