The heat flow on metric random walk spaces
DOI10.1016/j.jmaa.2019.123645zbMath1465.53053arXiv1806.01215OpenAlexW2805357710WikidataQ124848934 ScholiaQ124848934MaRDI QIDQ2287244
Julián Toledo, Marcos Solera, José M. Mazón Ruiz
Publication date: 20 January 2020
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1806.01215
random walksnonlocal operatorsOllivier-Ricci curvatureCheeger inequalitytransport inequalitiesBakry-Émery curvature-dimension condition
Sums of independent random variables; random walks (60G50) Heat equation (35K05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)
Related Items (12)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator
- Volume and diameter of a graph and Ollivier's Ricci curvature
- Displacement convexity of entropy and related inequalities on graphs
- Exact and asymptotic results on coarse Ricci curvature of graphs
- Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
- The heat content for nonlocal diffusion with non-singular kernels
- Dirichlet forms and symmetric Markov processes.
- Equivalent properties for CD inequalities on graphs with unbounded Laplacians
- Gradient flows of the entropy for finite Markov chains
- \(\lambda_ 1\), isoperimetric inequalities for graphs, and superconcentrators
- Ricci curvature of Markov chains on metric spaces
- Functional analysis, Sobolev spaces and partial differential equations
- Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
- Ricci curvature of finite Markov chains via convexity of the entropy
- Markov chains and invariant probabilities
- Transportation cost-information inequalities and applications to random dynamical systems and diffusions.
- A measure concentration inequality for contracting Markov chains
- Transportation cost for Gaussian and other product measures
- Ollivier's Ricci curvature and the coloring of graphs
- Gradient flows in metric random walk spaces
- Ollivier's Ricci curvature, local clustering and curvature-dimension inequalities on graphs
- Ricci curvature and eigenvalue estimate on locally finite graphs
- The total variation flow in metric random walk spaces
- On hyperboundedness and spectrum of Markov operators
- Modern approaches to discrete curvature
- Ricci curvature for metric-measure spaces via optimal transport
- Curvature and transport inequalities for Markov chains in discrete spaces
- Bipartite and neighborhood graphs and the spectrum of the normalized graph Laplace operator
- On the geometry of metric measure spaces. I
- Discrete Curvature and Abelian Groups
- Curvature aspects of graphs
- Transport inequalities, gradient estimates, entropy and Ricci curvature
- A simple proof of the blowing-up lemma (Corresp.)
- Difference Equations, Isoperimetric Inequality and Transience of Certain Random Walks
- A Curved Brunn--Minkowski Inequality on the Discrete Hypercube, Or: What Is the Ricci Curvature of the Discrete Hypercube?
- Analysis and Geometry of Markov Diffusion Operators
- Transport Inequalities. A Survey
- Isoperimetric Inequalities in Mathematical Physics. (AM-27)
- Optimal Transport
This page was built for publication: The heat flow on metric random walk spaces