Singularity of Full Scaling Limits of Planar Nearcritical Percolation

TL;DR

This paper investigates the full scaling limits of planar nearcritical percolation, demonstrating that different nearcritical parameters lead to singular limits, with results applicable to various lattice models.

Contribution

It establishes the singularity of nearcritical scaling limits with different parameters across general lattice models in the Quad-Crossing-Topology.

Findings

Different nearcritical parameters produce singular scaling limits.

Results apply to bond percolation on square lattice and site percolation on triangular lattice.

The study extends understanding of scaling limits in 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.