We prove that for , if is a 2-SLEpair in a simply connected domain D with an analytic boundary point , then as , converges to a positive number for some , which is called the two-curve Green’s function. The exponent α equals or depending on whether is one of the endpoints of or . We also find the convergence rate and the exact formula for the Green’s function up to a multiplicative constant. To derive these results, we construct two-dimensional diffusion processes and use orthogonal polynomials to obtain their transition density.
"Two-curve Green’s function for 2-SLE: the boundary case." Electron. J. Probab. 26 1 - 58, 2021. https://doi.org/10.1214/21-EJP592