Reflecting and absorbing boundary conditions on the tail of the Laplacian random walk

Abstract

The authors introduce a new version of the Laplacian random walk (LRW) for which the tail of the trajectory acts like a hard wall for incoming diffusing particles. They show how to implement these reflecting boundary conditions through the use of a modified discrete Laplace equation. From an exact enumeration on the square lattice they find that reflecting boundary conditions on the tail of the trajectory give rise to a denser fractal compared with the recently studied Laplacian random walk with absorbing boundary conditions.