Watermelons on the half-plane

Abstract We study the watermelon probabilities in uniform spanning forests on two-dimensional semi-infinite square lattice near either open or closed boundary to which can cannot be rooted, respectively. derive universal power laws describing asymptotic decay of these with distance between reference points growing infinity, as well their non-universal constant prefactors. The obtained exponents match previous predictions made for related dense polymer models using Coulomb gas technique and conformal field theory, calculations by other authors different settings. also discuss logarithmic corrections some argued appear correlation functions infinite lattice. show that full account diverging terms Green function, ensures correct probability normalization, provides pure law case studied here, discussed elsewhere. solution is based all-minors generalization Kirchhoff matrix tree theorem, image method developed expansion determinants.