I knew I should have taken that left turn at Albuquerque

Abstract

We study the Laplacian-infinity path as an extreme case of the Laplacian-alpha random walk. Although, in the finite alpha case, there is reason to believe that the process converges to SLE, we show that this is not the case when alpha is infinite. In fact, the scaling limit depends heavily on the lattice structure, and is not conformal (or even rotational) invariant.