Abstract
We prove that cluster observables of level-sets of the Gaussian free field on the hypercubic lattice Zd, d≥ 3 , are analytic on the whole off-critical regime R\ { h∗}. This result concerns in particular the percolation density function θ(h) and the (truncated) susceptibility χ(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≠ h∗, which we believe to be a result of independent interest. We also discuss the case of general transient graphs.
| Original language | English |
|---|---|
| Pages (from-to) | 187-223 |
| Number of pages | 37 |
| Journal | Communications in Mathematical Physics |
| Volume | 396 |
| Issue number | 1 |
| Early online date | 27 Jul 2022 |
| DOIs | |
| Publication status | Published - 1 Nov 2022 |
Bibliographical note
Funding Information:We are grateful to an anonymous referee for valuable comments on a prior version of this article. The second author would like to thank Subhajit Goswami, Alexis Prévost and Pierre-François Rodriguez for inspiring discussions on large deviations for GFF level-sets. This research was supported by the Swiss National Science Foundation and the NCCR SwissMAP. The second author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No 851565). The authors have no competing interests to declare that are relevant to the content of this article.
Publisher Copyright:
© 2022, The Author(s).
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics