We consider uniform spanning tree (UST) in topological rectangles with alternating boundary conditions. The Peano curves associated to the UST converge weakly to hypergeometric SLE8, denoted by hSLE8. From the convergence result, we obtain the continuity and reversibility of hSLE8 as well as an interesting connection between SLE8 and hSLE8. The loop-erased random walk (LERW) branch in the UST converges weakly to SLE2(−1,−1;−1,−1). We also obtain the limiting joint distribution of the two end points of the LERW branch.
QC 20250604