Propagators of random walks on comb lattices of arbitrary dimension

Abstract

We study diffusion on comb lattices of arbitrary dimension. Relying on the loopless structure of these lattices and using first-passage properties, we obtain exact and explicit formulae for the Laplace transforms of the propagators associated to nearest-neighbour random walks in both cases where either the first or the last point of the random walk is on the backbone of the lattice, and where the two extremities are arbitrarily chosen. As an application, we compute the mean-square displacement of a random walker on a comb of arbitrary dimension. We also propose an alternative and consistent approach of the problem using a master equation description, and obtain simple and generic expressions of the propagators. This method is more general and is extended to study the propagators of random walks on more complex comb-like structures. In particular, we study the case of a two-dimensional comb lattice with teeth of finite length.

References in corpus (3)

• Diffusion and subdiffusion of interacting particles on comb-like structures
• Random walks of molecular motors arising from diffusional encounters with immobilized filaments
• Mesoscopic description of random walks on combs

Cited by in corpus (7)

• Anomalous diffusion and FRAP dynamics in the random comb model
• Quantum subdiffusion with two- and three-body interactions
• From Particle Currents to Tracer Diffusion: Universal Correlation Profiles in Single-File Dynamics
• Non-Hermitian synthetic lattices with light-matter coupling
• Current fluctuations in the symmetric exclusion process beyond the one-dimensional geometry
• Displacement of transport processes on networked topologies
• Dynamics of soft interacting particles on a comb