Analyticity of Gaussian free field percolation observables
| Autor: | Panagiotis, Christoforos, Severo, Franco |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00220-022-04463-1 |
| Popis: | 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. Comment: 32 pages |
| Databáze: | arXiv |
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