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 $Lu(x)={\sum }_{y\in \mathbb{Z}}k(x-y)(u(y)-u(x))$ on the one-dimensional lattice with symmetric, integrable kernel $k$. We prove se…