TY - JOUR
T1 - A Particular Bit of Universality
T2 - Scaling Limits of Some Dependent Percolation Models
AU - Camia, Federico
AU - Newman, Charles M.
AU - Sidoravicius, Vladas
PY - 2004/4
Y1 - 2004/4
N2 - We study families of dependent site percolation models on the triangular lattice double struck T sign and hexagonal lattice ℍ 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 double struck T sign.
AB - We study families of dependent site percolation models on the triangular lattice double struck T sign and hexagonal lattice ℍ 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 double struck T sign.
UR - http://www.scopus.com/inward/record.url?scp=2142651448&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=2142651448&partnerID=8YFLogxK
U2 - 10.1007/s00220-004-1042-6
DO - 10.1007/s00220-004-1042-6
M3 - Article
AN - SCOPUS:2142651448
SN - 0010-3616
VL - 246
SP - 311
EP - 332
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -