2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95650A 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.ProbabilityMathematical Physics60K35, 82B41text