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The conjecture that the scaling limit of the two-dimensional self-avoidingwalk (SAW) in a half plane is given by the stochastic Loewner evolution (SLE)with $\kappa=8/3$ leads to explicit predictions about the SAW. A remarkablefeature of these predictions is that they yield not just critical exponents,but probability distributions for certain random variables associated with theself-avoiding walk. We test two of these predictions with Monte Carlosimulations and find excellent agreement, thus providing numerical support tothe conjecture that the scaling limit of the SAW is SLE$_{8/3}$.Comment: TeX file using APS REVTeX 4.0. 10 pages, 5 figures (encapsulated  postscript

Monte Carlo Tests of Stochastic Loewner Evolution Predictions for the 2D Self-Avoiding Walk