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Simulations of the self-avoiding walk (SAW) are performed in a half-plane anda cut-plane (the complex plane with the positive real axis removed) using thepivot algorithm. We test the conjecture of Lawler, Schramm and Werner that thescaling limit of the two-dimensional SAW is given by Schramm's StochasticLoewner Evolution (SLE). The agreement is found to be excellent. Thesimulations also test the conformal invariance of the SAW since conformalinvariance would imply that if we map the walks in the cut-plane into the halfplane using the conformal map z -> sqrt(z), then the resulting walks will havethe same distribution as the SAW in the half plane. The simulations showexcellent agreement between the distributions.Comment: Second version added more simulations and a proof of irreducibility.  25 pages, 16 figure

Conformal Invariance and Stochastic Loewner Evolution Predictions for the 2D Self-Avoiding Walk—Monte Carlo Tests