A generalization of Cardy's and Schramm's formulae

Mikhail Khristoforov; Mikhail Skopenkov; Stanislav Smirnov

doi:10.1007/s00220-025-05255-z

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arXiv · 2305.12368

A generalization of Cardy's and Schramm's formulae

Mikhail Khristoforov·Mikhail Skopenkov·Stanislav Smirnov

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Abstract

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.

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Mikhail Khristoforov, Mikhail Skopenkov, Stanislav Smirnov. 2023-05-21. A generalization of Cardy's and Schramm's formulae. https://doi.org/10.1007/s00220-025-05255-z

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