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arXiv · 2108.05294

Analyticity of Gaussian free field percolation observables

Christoforos Panagiotis·Franco Severo
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Abstract

We prove that cluster observables of level-sets of the Gaussian free field on the hypercubic lattice $\mathbb{Z}^d$, $d\geq3$, are analytic on the whole off-critical regime $\mathbb{R}\setminus\{h_*\}$. This result concerns in particular the percolation density function $\theta(h)$ and the (truncated) susceptibility $\chi(h)$. As an important step towards the proof, we show the exponential decay in probability for the capacity of a finite cluster for all $h\neq h_*$, which we believe to be a result of independent interest. We also discuss the case of general transient graphs.

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Christoforos Panagiotis, Franco Severo. 2021-08-11. Analyticity of Gaussian free field percolation observables. https://doi.org/10.1007/s00220-022-04463-1

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