Monte Carlo tests of stochastic Loewner evolution predictions for the 2D self-avoiding walk

The conjecture that the scaling limit of the two-dimensional self-avoiding walk (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 remarkable feature of these predictions is that they yield not just critical exponents but also probability distributions for certain random variables associated with the self-avoiding walk. We test two of these predictions with Monte Carlo simulations and find excellent agreement, thus providing numerical support to the conjecture that the scaling limit of the SAW is SLE(8/3).