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.

arXiv comment26 pages, 3 figures

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