A generalization of Cardy's and Schramm's formulae
arXiv:2305.12368 · doi:10.1007/s00220-025-05255-z
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.
14 pages, 6 figures