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 function Hilbert space harmonic function unbounded operator spectral theory Markov operator electrical network reproducing kernel Hilbert space graph Laplacian finite energy space dissipation space standard measure space path-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

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
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

This page was built for publication: New Hilbert space tools for analysis of graph Laplacians and Markov processes