On the scaling limit of planar self-avoiding walk
Probability
2007-05-23 v2 Mathematical Physics
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.
Keywords
Cite
@article{arxiv.math/0204277,
title = {On the scaling limit of planar self-avoiding walk},
author = {Gregory F. Lawler and Oded Schramm and Wendelin Werner},
journal= {arXiv preprint arXiv:math/0204277},
year = {2007}
}