Ricci Curvature on Birth-Death Processes

In this paper, we study curvature dimension conditions on birth-death processes which correspond to linear graphs, i.e., weighted graphs supported the infinite line or half line. We give a combinatorial characterization of Bakry and Émery’s CD(K,n) condition for prove triviality edge weights every graph Z with non-negative curvature. Moreover, show that decaying not faster than −R2 are stochastically complete. deduce type Bishop-Gromov comparison theorem normalized graphs. For curvature, obtain volume doubling property Poincaré inequality, yield Gaussian heat kernel estimates parabolic Harnack inequality by Delmotte’s result. As applications, generalize growth stochastic completeness properties weakly spherically symmetric Furthermore, examples positive lower bound.