Heat kernel and monotonicity inequalities on the graph

DOI10.1007/s12220-022-01093-wOpenAlexW4312056309MaRDI QIDQ2110278

Lin-Feng Wang

Publication date: 21 December 2022

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-022-01093-w

zbMATH Keywords

graphFisher informationheat kernelShannon entropy

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Measures of information, entropy (94A17) Information theory (general) (94A15) Heat kernel (35K08) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Monotonicity formulas via the Bakry-Émery curvature
• Remarks on curvature dimension conditions on graphs
• A new entropy formula for the linear heat equation
• Stochastic completeness for graphs with curvature dimension conditions
• A complete proof of the Poincaré and geometrization conjectures -- application of the Hamilton-Perelman theory of the Ricci flow
• Notes on Perelman's papers
• On the parabolic kernel of the Schrödinger operator
• The entropy formula for linar heat equation
• Li-Yau inequality on finite graphs via non-linear curvature dimension conditions
• Bakry-Émery curvature and diameter bounds on graphs
• Addenda to ``The entropy formula for linear heat equation
• New monotonicity formulas for Ricci curvature and applications. I
• Gradient estimates on connected graphs with the \(CD\psi (m,K)\) condition
• Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for non-negatively curved graphs
• Gradient estimates for the heat equation on graphs
• Li-Yau inequality for unbounded Laplacian on graphs
• Li-Yau inequality on graphs
• Buser's inequality on infinite graphs
• Monotonicity and its analytic and geometric implications