Path Laplacian operators and superdiffusive processes on graphs. II. two-dimensional lattice. (English) Zbl 06914735
Summary: 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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