New Hilbert space tools for analysis of graph Laplacians and Markov processes

DOI10.1007/s11785-023-01412-1OpenAlexW4386935588MaRDI QIDQ6081653

Palle E. T. Jorgensen, Sergey Bezuglyi

Publication date: 5 October 2023

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-023-01412-1

zbMATH Keywords

Green's functionHilbert spaceharmonic functionunbounded operatorspectral theoryMarkov operatorelectrical networkreproducing kernel Hilbert spacegraph Laplacianfinite energy spacedissipation spacestandard measure spacepath-space measure

Mathematics Subject Classification ID

Dirichlet forms (31C25) Probabilistic potential theory (60J45) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Dual spaces of operator algebras (47L50)

Cites Work

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• A discrete Gauss-Green identity for unbounded Laplace operators, and the transience of random walks
• Conditional measures and conditional expectation; Rohlin's disintegration theorem
• Convergent sequences of dense graphs. II. Multiway cuts and statistical physics
• Reproducing kernel Hilbert spaces generated by the binomial coefficients
• Symmetric pairs and self-adjoint extensions of operators, with applications to energy networks
• Determinantal point processes associated with Hilbert spaces of holomorphic functions
• A Hilbert space approach to effective resistance metric
• A class of Gaussian processes with fractional spectral measures
• Geometry and analysis of Dirichlet forms
• Conservativeness criteria for generalized Dirichlet forms
• Theory of reproducing kernels and applications
• Dirichlet norms, capacities and generalized isoperimetric inequalities for Markov operators.
• Denumerable Markov chains. Generating functions, boundary theory, random walks on trees.
• Geometry on probability spaces
• Determinantal processes and completeness of random exponentials: the critical case
• Convergent sequences of dense graphs. I: Subgraph frequencies, metric properties and testing
• Introduction to the theory of (non-symmetric) Dirichlet forms
• Transfer operators, endomorphisms, and measurable partitions
• Symmetric pairs of unbounded operators in Hilbert space, and their applications in mathematical physics
• Representations of higher-rank graph \(C^\ast\)-algebras associated to {\(\Lambda\)}-semibranching function systems
• On Dirichlet processes associated with second order divergence form operators
• Determinantal probability measures
• Topics in orbit equivalence
• Semi-Dirichlet forms and Markov processes
• Purely atomic representations of higher-rank graph \(C^*\)-algebras
• Graph Laplace and Markov operators on a measure space
• The ASEP and determinantal point processes
• On the equivalence of probability spaces
• Hyperfinite Dirichlet forms and stochastic processes
• A trace theorem for the Dirichlet form on the Sierpinski gasket
• Online learning algorithms
• Unbounded graph-Laplacians in energy space, and their extensions
• Learning theory estimates via integral operators and their approximations
• Discrete reproducing kernel Hilbert spaces: Sampling and distribution of Dirac-masses
• Moment problems in an infinite number of variables
• Spectral Theory for Gaussian Processes: Reproducing Kernels, Boundaries, and L²-Wavelet Generators with Fractional Scales
• An Introduction to the Theory of Reproducing Kernel Hilbert Spaces
• Quasi regular Dirichlet forms and the stochastic quantization problem
• Bratteli diagrams: Structure, measures, dynamics
• Probability on Trees and Networks
• Stochastic Processes Induced by Singular Operators
• Spectral comparisons between networks with different conductance functions
• Non-commutative Analysis
• Relative reproducing kernel Hilbert spaces
• Bounds on the L 2 Spectrum for Markov Chains and Markov Processes: A Generalization of Cheeger's Inequality
• Characterization of Positive Reproducing Kernels. Applications to Green's Functions
• General Irreducible Markov Chains and Non-Negative Operators
• Learning Theory
• Conditionally strictly negative definite kernels
• ONLINE LEARNING WITH MARKOV SAMPLING
• Lévy Processes and Stochastic Calculus
• Convergence Rates for Approximate Eigenvalues of Compact Integral Operators
• Conversion from Nonstandard to Standard Measure Spaces and Applications in Probability Theory
• Ergodic Equivalence Relations, Cohomology, and Von Neumann Algebras. I
• Ergodic Equivalence Relations, Cohomology, and Von Neumann Algebras. II
• Ergodic decomposition of quasi-invariant probability measures
• COUNTABLE BOREL EQUIVALENCE RELATIONS
• Modular estimates of fractional integral operators andk-plane transforms
• Nonuniform sampling, reproducing kernels, and the associated Hilbert spaces
• Homogenization in Random Dirichlet Forms
• 𝑊-Markov measures, transfer operators, wavelets and multiresolutions
• ORDERED BRATTELI DIAGRAMS, DIMENSION GROUPS AND TOPOLOGICAL DYNAMICS
• Markov Processes Associated With Positivity Preserving Coercive Forms
• Random Walks on Infinite Graphs and Groups
• Resistance Boundaries of Infinite Networks
• On new fractal phenomena connected with infinite linear IFS
• Learning Discrete Bayesian Networks from Continuous Data
• Graphons, cut norm and distance, couplings and rearrangements
• Infinite Product Representations for Kernels and Iterations of Functions
• Combinatorics on Bratteli diagrams and dynamical systems
• Metric Spaces and Positive Definite Functions
• Theory of Reproducing Kernels

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