Two interacting diffusing particles on low-dimensional discrete structures

In this paper we study the motion of two particles diffusing on lowdimensional discrete structures in presence of a hard-core repulsive interaction. We show that the problem can be mapped in two decoupled problems of single particles diffusing on different graphs by a transformation we call diffusion graph transform. This technique is applied to study two specific cases: the narrow comb and the ladder lattice. We focus on the determination of the long time probabilities for the contact between particles and their reciprocal crossing. We also obtain the mean square dispersion of the particles in the case of the narrow comb lattice. The case of a sticking potential and of ‘vicious’ particles are discussed.