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.

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