E. Estrada, E. Hameed, M. Langer and A. Puchalska,
Path Laplacian operators and superdiffusive processes on graphs. II.
Two-dimensional lattice,
Linear Algebra Appl. 555 (2018), 373–397
Abstract:
In this paper we consider a generalized diffusion equation on a square lattice
corresponding to Mellin transforms of the k-path Laplacian.
In particular, we prove that superdiffusion occurs when the parameter s
in the Mellin transform is in the interval (2,4) and that normal diffusion
prevails when s > 4.