By analogy with Carleson's observation on Cardy's formula describing crossing probabilities for the scaling limit of critical percolation, we exhibit ``privileged geometries'' for Stochastic Loewner Evolutions with various parameters, for which certain hitting distributions are uniformly distributed. We then examine consequences for limiting probabilities of events concerning various critical plane discrete models.
"SLE and Triangles." Electron. Commun. Probab. 8 28 - 42, 2003. https://doi.org/10.1214/ECP.v8-1067