Singularity of Full Scaling Limits of Planar Nearcritical Percolation

Abstract

We consider full scaling limits of planar nearcritical percolation in the Quad-Crossing-Topology introduced by Schramm and Smirnov. We show that two nearcritical scaling limits with different parameters are singular with respect to each other. The results hold for percolation models on rather general lattices, including bond percolation on the square lattice and site percolation on the triangular lattice.

12 pages, minor changes

References in corpus (4)

• Two-Dimensional Critical Percolation: The Full Scaling Limit
• On the scaling limits of planar percolation
• Free subalgebras of quotient rings of Ore extensions
• Singularity of Nearcritical Percolation Exploration Paths

Cited by in corpus (1)

• Convergence of Fermionic Observables in the Massive Planar FK-Ising Model