A Particular Bit of Universality: Scaling Limits of Some Dependent Percolation Models

We study families of dependent site percolation models on the triangular lattice and hexagonal lattice that arise by applying certain cellular automata to independent percolation configurations. We analyze the scaling limit of such models and show that the distance between macroscopic portions of cluster boundaries of any two percolation models within one of our families goes to zero almost surely in the scaling limit. It follows that each of these cellular automaton generated dependent percolation models has the same scaling limit (in the sense of Aizenman-Burchard [3]) as independent site percolation on .The work was conducted while this author was at Department of Physics, New York University, New York, NY 10003, USA. Research partially supported by the U.S. NSF under grants DMS-98-02310 and DMS-01-02587.Research partially supported by the U.S. NSF under grants DMS-98-03267 and DMS-01-04278.Research partially supported by FAPERJ grant E-26/151.905/2000 and CNPq.