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arXiv:2305.12368 [math.PR]AbstractReferencesReviewsResources

A generalization of Cardy's and Schramm's formulae

Mikhail Khristoforov, Mikhail Skopenkov, Stanislav Smirnov

Published 2023-05-21Version 1

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.

Comments: 14 pages, 6 figures
Categories: math.PR, math-ph, math.CV, math.MP
Subjects: 60K35, 30C30, 33C05, 81T40, 82B43
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