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arXiv · 1903.00517

Curvature-dimension inequalities for non-local operators in the discrete setting

Adrian Spener·Frederic Weber·Rico Zacher
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Abstract

We study Bakry-\'Emery curvature-dimension inequalities for non-local operators on the one-dimensional lattice and prove that operators with finite second moment have finite dimension. Moreover, we show that a class of operators related to the fractional Laplacian fails to have finite dimension and establish both positive and negative results for operators with sparsely supported kernels. Moreover, a large class of operators is shown to have no positive curvature. The results correspond to CD inequalities on locally infinite graphs.

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Adrian Spener, Frederic Weber, Rico Zacher. 2019-03-01. Curvature-dimension inequalities for non-local operators in the discrete setting. https://arxiv.org/abs/1903.00517

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