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Li-Yau and Harnack inequalities via curvature-dimension conditions for discrete long-range jump operators including the fractional discrete Laplacian
Sebastian Kräss, Frederic Weber, Rico Zacher
We consider operators of the form on the one-dimensional lattice with symmetric, integrable kernel . We prove se…
Li-Yau inequalities for general non-local diffusion equations via reduction to the heat kernel
Frederic Weber, Rico Zacher
We establish a reduction principle to derive Li-Yau inequalities for non-local diffusion problems in a very general framework, which covers both the discrete and continuous setting…
The Fractional Laplacian has Infinite Dimension
Adrian Spener, Frederic Weber, Rico Zacher
We show that the fractional Laplacian on fails to satisfy the Bakry-Émery curvature-dimension inequality for all curvature bounds and all…
Curvature-dimension inequalities for non-local operators in the discrete setting
Adrian Spener, Frederic Weber, Rico Zacher
We study Bakry-Émery curvature-dimension inequalities for non-local operators on the one-dimensional lattice and prove that operators with finite second moment have finite dimensio…