An application of the Bakry-Emery criterion to infinite dimensional diffusions

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For Riemannian manifolds with a measure (M, g, e − f dvol g ) we prove mean curvature and volume comparison results when the ∞ - Bakry-Emery Ricci tensor is bounded from below and f

We will use the idea of Bakry and Emery [1] to give a notion of a ”lower Ricci curvature bound” on graphs and to prove that Ricci curvature on Locally finite graphs is always