Inhomogeneity and universality: off-critical behavior of interfaces

TL;DR

This paper investigates the behavior of interfaces in inhomogeneous systems, identifying a characteristic length in gradient percolation that enables the construction of scaling limits resembling off-critical percolation interfaces, revealing new insights into their universality.

Contribution

It introduces a characteristic length for gradient percolation, refining previous estimates and enabling the construction of non-trivial scaling limits with off-critical properties.

Findings

Identified a characteristic length scale in gradient percolation.

Constructed non-trivial scaling limits of interfaces.

Showed local behavior resembles off-critical percolation interfaces.

Abstract

We further study the interfaces arising in a situation of inhomogeneity. More precisely, we identify a characteristic length for the gradient percolation model, that enables us to tighten previous estimates established for it. This allows to construct non-trivial scaling limits: the limiting objects share some properties with critical percolation interfaces, but locally, they rather behave like off-critical percolation interfaces.