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

I knew I should have taken that left turn at Albuquerque