The Fractional Laplacian has Infinite Dimension

Abstract

We show that the fractional Laplacian on ${\mathbb{R}}^d$ fails to satisfy the Bakry-Émery curvature-dimension inequality $CD(\kappa ,N)$ for all curvature bounds $\kappa \in \mathbb{R}$ and all finite dimensions $N>0$.

14 pages, 2 figures