Chemical Distance for the Level Sets of the Gaussian Free Field

Tal Peretz

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arXiv · 2501.02881

Chemical Distance for the Level Sets of the Gaussian Free Field

Tal Peretz

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Abstract

We consider the Gaussian free field $\varphi$ on $\mathbb{Z}^d$ for $d \geq 3$ and study the level sets $\{\varphi \geq h \}$ in the percolating regime. We prove upper and lower bounds for the probability that the chemical distance is much larger than Euclidean distance. Our proof uses a renormalization scheme combined with a bootstrap argument.

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Tal Peretz. 2025-01-06. Chemical Distance for the Level Sets of the Gaussian Free Field. https://arxiv.org/abs/2501.02881

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