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On the chemical distance exponent for the two-sided level-set of the 2D Gaussian free field
Yifan Gao, Fuxi Zhang · 2020-11-10 · via math.PR updates on arXiv.org

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.

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