On the scaling limit of planar self-avoiding walk

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 nondisconnecting Brownian motions. New heuristic derivations are given for the critical exponents for SAWs and SAPs. See link below.