Convergence to global equilibrium for Fokker-Planck equations on a graph and Talagrand-type inequalities

DOI10.1016/j.jde.2016.05.003zbMath1341.37030arXiv1409.0711OpenAlexW2964304761MaRDI QIDQ288752

Wen Huang, Prasad Tetali, Rui Che, Yao Li

Publication date: 27 May 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.0711

zbMATH Keywords

graphFokker-Planck equationGibbs densityTalagrand inequality

Mathematics Subject Classification ID

Diffusion processes (60J60) Generation, random and stochastic difference and differential equations (37H10) Continuous-time Markov processes on discrete state spaces (60J27) Dynamical systems involving maps of trees and graphs (37E25)

Related Items (5)

Entropy dissipation of Fokker-Planck equations on graphs ⋮ Influence prediction for continuous-time information propagation on networks ⋮ Entropy dissipation semi-discretization schemes for Fokker-Planck equations ⋮ Entropic Ricci Curvature for Discrete Spaces ⋮ The Łojasiewicz inequality for free energy functionals on a graph

Cites Work

• Unnamed Item
• Unnamed Item
• On gradient structures for Markov chains and the passage to Wasserstein gradient flows
• Geodesic convexity of the relative entropy in reversible Markov chains
• Gradient flows of the entropy for finite Markov chains
• Lower bounds of the Laplacian spectrum of graphs based on diameter
• A nontrivial upper bound on the largest Laplacian eigenvalue of weighted graphs
• Modified logarithmic Sobolev inequalities in discrete settings
• The Fokker-Planck equation. Methods of solution and applications.
• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
• Lower bounds for the eigenvalues of Laplacian matrices
• Hypercontractivity of Hamilton-Jacobi equations.
• Ricci curvature of finite Markov chains via convexity of the entropy
• Fokker-Planck equations for a free energy functional or Markov process on a graph
• Hamilton-Jacobi semigroup on length spaces and applications
• Ricci curvature for metric-measure spaces via optimal transport
• The sub-Gaussian constant and concentration inequalities
• Lower bounds of the Laplacian graph eigenvalues
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems
• Concentration on the Discrete Torus Using Transportation
• Singular Perturbation Methods in Stochastic Differential Equations of Mathematical Physics
• The Variational Formulation of the Fokker--Planck Equation
• Optimal Transport
• Handbook of stochastic methods for physics, chemistry and the natural sciences.

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