On the chemical distance exponent for the two-sided level-set of the 2D Gaussian free field

Abstract

In this paper we introduce the two-sided level-set for the two-dimensional discrete Gaussian free field. Then we investigate the chemical distance for the two-sided level-set percolation. Our result shows that the chemical distance should have dimension strictly larger than $1$, which in turn stimulates some tempting questions about the two-sided level-set.

26 pages, 3 figures

References in corpus (2)

• On the scaling of the chemical distance in long-range percolation models
• Strict inequality for the chemical distance exponent in two-dimensional critical percolation