Renormalised two-point functions of CLE$_4$ gaskets
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917414105513984 |
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| author | Aru, Juhan Lupu, Titus |
| author_facet | Aru, Juhan Lupu, Titus |
| contents | We consider nested CLE$_4$ in a simply-connected domain and compute the following renormalised probabilities: the probability that two points belong to the same CLE$_4$ gasket and the probability that two points belong to the outermost CLE$_4$ gasket. While the integrability is rooted in the conformal field theory of the Ashkin-Teller (AT) model, we provide a purely probabilistic calculation via Brownian loop soups and the geometry of the 2D continuum Gaussian free field. More generally, we also calculate renormalised probabilities that two points belong to CLE$_4$ gaskets sampled in alternation with certain two-valued sets of the Gaussian free field. These quantities correspond to the two-point function of the conjectured scaling limit of the AT single spins on the critical line. At the decoupling point, our results recover the Ising model correlations and suggest a CLE$_4$-based FK representation of the AT spin model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15146 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Renormalised two-point functions of CLE$_4$ gaskets Aru, Juhan Lupu, Titus Probability Mathematical Physics We consider nested CLE$_4$ in a simply-connected domain and compute the following renormalised probabilities: the probability that two points belong to the same CLE$_4$ gasket and the probability that two points belong to the outermost CLE$_4$ gasket. While the integrability is rooted in the conformal field theory of the Ashkin-Teller (AT) model, we provide a purely probabilistic calculation via Brownian loop soups and the geometry of the 2D continuum Gaussian free field. More generally, we also calculate renormalised probabilities that two points belong to CLE$_4$ gaskets sampled in alternation with certain two-valued sets of the Gaussian free field. These quantities correspond to the two-point function of the conjectured scaling limit of the AT single spins on the critical line. At the decoupling point, our results recover the Ising model correlations and suggest a CLE$_4$-based FK representation of the AT spin model. |
| title | Renormalised two-point functions of CLE$_4$ gaskets |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2604.15146 |