{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:06:20Z","timestamp":1760148380103,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T00:00:00Z","timestamp":1682467200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NSFC","award":["11401106"],"award-info":[{"award-number":["11401106"]}]},{"name":"German National Merit Foundation","award":["11401106"],"award-info":[{"award-number":["11401106"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we study curvature dimension conditions on birth-death processes which correspond to linear graphs, i.e., weighted graphs supported on the infinite line or the half line. We give a combinatorial characterization of Bakry and \u00c9mery\u2019s CD(K,n) condition for linear graphs and prove the triviality of edge weights for every linear graph supported on the infinite line Z with non-negative curvature. Moreover, we show that linear graphs with curvature decaying not faster than \u2212R2 are stochastically complete. We deduce a type of Bishop-Gromov comparison theorem for normalized linear graphs. For normalized linear graphs with non-negative curvature, we obtain the volume doubling property and the Poincar\u00e9 inequality, which yield Gaussian heat kernel estimates and parabolic Harnack inequality by Delmotte\u2019s result. As applications, we generalize the volume growth and stochastic completeness properties to weakly spherically symmetric graphs. Furthermore, we give examples of infinite graphs with a positive lower curvature bound.<\/jats:p>","DOI":"10.3390\/axioms12050428","type":"journal-article","created":{"date-parts":[[2023,4,27]],"date-time":"2023-04-27T02:18:34Z","timestamp":1682561914000},"page":"428","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Ricci Curvature on Birth-Death Processes"],"prefix":"10.3390","volume":"12","author":[{"given":"Bobo","family":"Hua","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, LMNS, Fudan University, Shanghai 200433, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Florentin","family":"M\u00fcnch","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Potsdam, 14469 Potsdam, Germany"},{"name":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,26]]},"reference":[{"key":"ref_1","first-page":"55","article-title":"The heat equation on noncompact Riemannian manifolds","volume":"182","year":"1991","journal-title":"Mat. 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