Analytic-geometric methods for finite Markov chains with applications to quasi-stationarity

zbMath1456.60176arXiv1906.04877MaRDI QIDQ5140270

Persi Diaconis, Kelsey Houston-Edwards, Laurent Saloff-Coste

Publication date: 15 December 2020

Full work available at URL: https://arxiv.org/abs/1906.04877

zbMATH Keywords

Harnack inequalityMarkov chainsinner-uniform domains

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

Related Items

Polynomial rate of convergence to the Yaglom limit for Brownian motion with drift, The 4-Player Gambler’s Ruin Problem, Gambler's ruin estimates on finite inner uniform domains, Decay of harmonic functions for discrete time Feynman--Kac operators with confining potentials, Convergence to quasi-stationarity through Poincaré inequalities and Bakry-Émery criteria

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
• The central limit theorem in Lipschitz domains
• Scale-invariant boundary Harnack principle in inner uniform domains
• Dirichlet forms and symmetric Markov processes.
• The discrete and classical Dirichlet problem
• Nash inequalities for finite Markov chains
• On the existence of boundary values for harmonic functions in several variables
• Intrinsic ultracontractivity via capacitary width
• Scale-invariant boundary Harnack principle on inner uniform domains in fractal-type spaces
• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• Exit times from cones in \({\mathbb{R}}^ n\) of Brownian motion
• Intrinsic ultracontractivity and the Dirichlet Laplacian
• Hölder domains and the boundary Harnack principle
• Exit times of Brownian motion, harmonic majorization, and Hardy spaces
• Principle de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien
• Estimates of harmonic measure
• Random walks on finite convex sets of lattice points
• What do we know about the Metropolis algorithm?
• Parabolic Harnack inequality and estimates of Markov chains on graphs
• Comparison theorems for reversible Markov chains
• Comparison techniques for random walk on finite groups
• Intrinsic ultracontractivity of Dirichlet Laplacians in non-smooth domains
• Moderate growth and random walk on finite groups
• The spectrum of the continuous Laplacian on a graph
• A geometric interpretation of the Metropolis-Hastings algorithm.
• Parabolic Harnack inequality on fractal-type metric measure Dirichlet spaces
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Analysis on geodesic balls of sub-elliptic operators
• The Dirichlet heat kernel in inner uniform domains: local results, compact domains and non-symmetric forms
• Lumpings of algebraic Markov chains arise from subquotients
• Random walks in cones
• The discrete and classical Dirichlet problem. II
• Monte Carlo strategies in scientific computing.
• Quasi-Stationary Distributions
• Random Walks and Heat Kernels on Graphs
• Inégalité de Harnack elliptique sur les graphes
• Equivalence between the boundary Harnack principle and the Carleson estimate
• Injectivity theorems in plane and space
• Markov Chains
• Stability of parabolic Harnack inequalities
• Introduction to Analysis on Graphs
• Volume growth and stochastic completeness of graphs
• A boundary harnack principle for lipschitz domains and the principle of positive singularities
• Characterization of sub‐Gaussian heat kernel estimates on strongly recurrent graphs
• Boundary Harnack principle and Martin boundary for a uniform domain
• On quantitative convergence to quasi-stationarity