A generalization of Cardy's and Schramm's formulae
Probability
2025-04-22 v1 Mathematical Physics
Complex Variables
math.MP
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.
Keywords
Cite
@article{arxiv.2305.12368,
title = {A generalization of Cardy's and Schramm's formulae},
author = {Mikhail Khristoforov and Mikhail Skopenkov and Stanislav Smirnov},
journal= {arXiv preprint arXiv:2305.12368},
year = {2025}
}
Comments
14 pages, 6 figures