Three-leg correlations in the two-component spanning tree on the upper half-plane

Abstract

We present a detailed asymptotic analysis of correlation functions for thetwo-component spanning tree on the two-dimensional lattice when one componentcontains three paths connecting vicinities of two fixed lattice sites at large distances apart. We extend the known result for correlations on the plane to the case of the upper half-planewith closed and open boundary conditions. We found asymptotics of correlations for distancer from the boundary to one of the fixed lattice sites for the cases and .