Boundary four-point connectivities of conformal loop ensembles
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917385248702464 |
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| author | Cai, Gefei |
| author_facet | Cai, Gefei |
| contents | We derive the boundary four-point Green's functions for conformal loop ensembles (CLE) with $κ\in(4,8)$. Specializing to $κ=6$ and $κ=16/3$, we establish the exact formulas for the boundary four-point connectivities in critical Bernoulli percolation and the FK-Ising model conjectured by Gori-Viti (2017, 2018). In particular, we identify a logarithmic singularity in the critical FK-Ising model. Our approach also applies to the one-bulk and two-boundary connectivities of CLE, thereby extending the factorization formula of Beliaev-Izyurov (2012) to all $κ\in(4,8)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28161 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Boundary four-point connectivities of conformal loop ensembles Cai, Gefei Probability Mathematical Physics 60J67, 60K35 We derive the boundary four-point Green's functions for conformal loop ensembles (CLE) with $κ\in(4,8)$. Specializing to $κ=6$ and $κ=16/3$, we establish the exact formulas for the boundary four-point connectivities in critical Bernoulli percolation and the FK-Ising model conjectured by Gori-Viti (2017, 2018). In particular, we identify a logarithmic singularity in the critical FK-Ising model. Our approach also applies to the one-bulk and two-boundary connectivities of CLE, thereby extending the factorization formula of Beliaev-Izyurov (2012) to all $κ\in(4,8)$. |
| title | Boundary four-point connectivities of conformal loop ensembles |
| topic | Probability Mathematical Physics 60J67, 60K35 |
| url | https://arxiv.org/abs/2603.28161 |