Conformal invariance of loop erased percolation
I will start by reviewing the loop-erased random walk (LERW). In this model one takes a nearest neighbor random walk and erases the loops it forms in chronological order. The path that is left is a walk with no self-intersections. It has been proved to converge to SLE_2 as the lattice spacing goes to zero. (I will give a very quick definition of SLE.) This serves as background and motivation for considering a model in which we erase the loops in a percolation interface to obtain a curve without self-intersections. Monte Carlo simulations of this model provide good evidence that the resulting random curve is conformally invariant. The simulations also indicate it has the same fractal dimension as SLE_8/3, but it is not SLE_8/3.