Singularity of Nearcritical Percolation Exploration Paths
arXiv:1110.4203
Abstract
We show that the laws of scaling limits of nearcritical percolation exploration paths with different parameters are singular with respect to each other. This generalises a result of Nolin and Werner, using a similar technique. As a corollary, the singularity can even be detected from an infinitesimal initial segment. Moreover, nearcritical scaling limits of exploration paths are mutually singular under scaling maps.
23 pages, 7 figures; an expository section added and minor changes