Analyticity of Gaussian Free Field Percolation Observables
نویسندگان
چکیده
We prove that cluster observables of level-sets the Gaussian free field on hypercubic lattice $\mathbb{Z}^d$, $d\geq3$, are analytic whole off-critical regime $\mathbb{R}\setminus\{h_*\}$. This result concerns in particular percolation density function $\theta(h)$ and (truncated) susceptibility $\chi(h)$. As an important step towards proof, we show exponential decay probability for capacity a finite all $h\neq h_*$, which believe to be independent interest. also discuss case general transient graphs.
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2022
ISSN: ['0010-3616', '1432-0916']
DOI: https://doi.org/10.1007/s00220-022-04463-1