A generalization of Cardy's and Schramm's formulae
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915250072190976 |
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| author | Khristoforov, Mikhail Skopenkov, Mikhail Smirnov, Stanislav |
| author_facet | Khristoforov, Mikhail Skopenkov, Mikhail Smirnov, Stanislav |
| contents | We study critical site percolation on the triangular lattice. We find the difference of the probabilities of having a percolation interface to the right and to the left of two given points in the scaling limit. This generalizes both Cardy's and Schramm's formulae. The generalization involves a new interesting discrete analytic observable and an unexpected conformal mapping. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_12368 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A generalization of Cardy's and Schramm's formulae Khristoforov, Mikhail Skopenkov, Mikhail Smirnov, Stanislav Probability Mathematical Physics Complex Variables 60K35, 30C30, 33C05, 81T40, 82B43 We study critical site percolation on the triangular lattice. We find the difference of the probabilities of having a percolation interface to the right and to the left of two given points in the scaling limit. This generalizes both Cardy's and Schramm's formulae. The generalization involves a new interesting discrete analytic observable and an unexpected conformal mapping. |
| title | A generalization of Cardy's and Schramm's formulae |
| topic | Probability Mathematical Physics Complex Variables 60K35, 30C30, 33C05, 81T40, 82B43 |
| url | https://arxiv.org/abs/2305.12368 |