SLE boundary visits
The present paper deals with the probabilities with which chordal Schramm-Loewner evolutions (SLE) visit small neighborhoods of boundary points. The authors employ a method based on quantum group calculations which allow them to explicitly calculate solutions of the chordal SLE\(_k\) boundary visit probability amplitudes. The solutions are expressed in terms of linear combinations of Coulomb gas integrals and can be transformed into regularized real integrals. Here, the authors also use the technique of a spin chain-Coulomb gas correspondence between tensor product representations of a quantum group and functions given by Dotsenko-Fateev type integrals. In particular, the obtained formulas are applied to the renormalized scaling limit boundary visit probabilities for lattice model interfaces. The results are compared with numerical simulations of percolation, loop-erased random walks, and Fortuin-Kasteleyn random cluster models.
scientific article; zbMATH DE number 6592861
scientific article