Entropic Ricci curvature bounds for discrete interacting systems
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Summary
A new and systematic method for proving entropic Ricci curvature lower bounds for Markov chains on discrete sets is developed, inspired by recent work of Caputo, Dai Pra and Posta on discrete functional inequalities.
- Type
- article
- Published
- 2015-01-03
- Cited by
- 74
- References
- 27
- Access
- Open access
- OpenAlex
- https://openalex.org/W303747730
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:55275445
Keywords
Ricci curvature, Mathematics, Bernoulli's principle, Curvature, Markov chain
References
- Ricci curvature for metric-measure spaces via optimal transport
- Mass transportation and rough curvature bounds for discrete spaces
- Modified Logarithmic Sobolev Inequalities in Discrete Settings
- Spectral gap for the zero range process with constant rate
- Gromov-Hausdorff Convergence of Discrete Transportation Metrics
- Gradient flows of the entropy for finite Markov chains
- On the geometry of metric measure spaces. II
- Entropy dissipation estimates in a zero-range dynamics
- Entropy decay for interacting systems via the Bochner-Bakry-Émery approach
- Gradient flow structures for discrete porous medium equations
- Exponential decay of entropy in the random transposition and Bernoulli-Laplace models
- Ricci curvature and eigenvalue estimate on locally finite graphs
- Ricci Curvature of Finite Markov Chains via Convexity of the Entropy
- Spectral gap estimates for interacting particle systems via a Bochner-type identity
- THE VARIATIONAL FORMULATION OF THE FOKKER-PLANCK EQUATION
- A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems
- Ricci curvature of Markov chains on metric spaces
- Convex entropy decay via the Bochner-Bakry-Emery approach
- Geodesic convexity of the relative entropy in reversible Markov chains
- Fokker–Planck Equations for a Free Energy Functional or Markov Process on a Graph
Cited by
- A discrete log-Sobolev inequality under a Bakry-Emery type condition
- Long-time behavior of a finite volume discretization for a fourth order diffusion equation
- Ricci curvature bounds for weakly interacting Markov chains
- Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance
- A large deviation perspective on exponential decay of entropy and lower bounds on the Ricci-curvature
- Displacement convexity for the entropy in semi-discrete non-linear Fokker–Planck equations
- Gromov–Hausdorff limit of Wasserstein spaces on point clouds
- Nonlinear Fokker-Planck equations on graphs and their asymptotic properties
- Lower Bound for the Coarse Ricci Curvature of Continuous-Time Pure-Jump Processes
- Distance Bounds for Graphs with Some Negative Bakry-Émery Curvature
- A discrete Bakry-Emery method and its application to the porous-medium equation
- Constant curvature metrics for Markov chains
- Cutoff for the mean-field zero-range process with bounded monotone rates
- On the geometry of geodesics in discrete optimal transport
- Super Ricci flows for weighted graphs
- Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians
- Entropy dissipation of Fokker-Planck equations on graphs
- A Noncommutative Transport Metric and Symmetric Quantum Markov Semigroups as Gradient Flows of the Entropy
- Scaling Limits of Discrete Optimal Transport
- Non-commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems
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