Cluster Expansions for GIBBS Point Processes

DOI10.1017/apr.2019.46zbMath1427.60202arXiv1807.10725OpenAlexW2883621402WikidataQ126807817 ScholiaQ126807817MaRDI QIDQ5203978

No author found.

Publication date: 9 December 2019

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.10725

zbMATH Keywords

cumulantsbranching processcluster expansionBoolean percolationGibbs point process

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Classical equilibrium statistical mechanics (general) (82B05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items

Virial series for a system of classical particles interacting through a pair potential with negative minimum ⋮ A variational framework for the inverse Henderson problem of statistical mechanics ⋮ Strong spatial mixing for repulsive point processes ⋮ An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions ⋮ Convergence of cluster and virial expansions for repulsive classical gases ⋮ Structural properties of Gibbsian point processes in abstract spaces ⋮ On the analyticity of the pressure for a non-ideal gas with high density boundary conditions ⋮ On the uniqueness of Gibbs distributions with a non-negative and subcritical pair potential ⋮ Disagreement coupling of Gibbs processes with an application to Poisson approximation ⋮ Analyticity for classical gasses via recursion ⋮ Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics ⋮ Cluster expansions: necessary and sufficient convergence conditions ⋮ Revisiting Groeneveld’s approach to the virial expansion ⋮ Virial inversion and density functionals ⋮ Penrose-stable interactions in classical statistical mechanics ⋮ Classical particles in the continuum subjected to high density boundary conditions

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
• Spectral gap for Glauber type dynamics for a special class of potentials
• Gibbs point process approximation: total variation bounds using Stein's method
• The Papangelou process
• Existence of Gibbsian point processes with geometry-dependent interactions
• Cluster and virial expansions for the multi-species Tonks gas
• Wiener chaos: Moments, cumulants and diagrams. A survey with computer implementation
• On the convergence of cluster expansions for polymer gases
• Combinatorics and cluster expansions
• Cluster expansion for abstract polymer models
• Gibbs measures and phase transitions
• Random fields
• A remark on the connection between the large deviation principle and the central limit theorem
• Large deviations and the maximum entropy principle for marked point random fields
• Stochastic integrals: A combinatorial approach
• The random connection model in high dimensions
• The gas phase of continuous systems of hard spheres interacting via \(n\)-body potential.
• The spectral gap for a Glauber-type dynamics in a continuous gas
• Convergence of density expansions of correlation functions and the Ornstein-Zernike equation
• Well-posedness of the iterative Boltzmann inversion
• Loss network representation of Peierls contours
• Fast approximation of the intensity of Gibbs point processes
• Disagreement percolation for the hard-sphere model
• Disagreement percolation for Gibbs ball models
• Convergence of Mayer and Virial expansions and the Penrose tree-graph identity
• The analyticity region of the hard sphere gas. Improved bounds
• Cluster expansion for abstract polymer models. New bounds from an old approach
• Glauber dynamics of continuous particle systems
• The repulsive lattice gas, the independent-set polynomial, and the Lovász local lemma
• Superstable interactions in classical statistical mechanics
• Gibbs states of continuum particle systems with unbounded spins: Existence and uniqueness
• Abstract cluster expansion with applications to statistical mechanical systems
• Integral and Differential Characterizations of the GIBBS Process
• An Introduction to the Theory of Point Processes
• GIBBS MEASURES OF CONTINUOUS SYSTEMS: AN ANALYTIC APPROACH
• Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics
• Moments and Central Limit Theorems for Some Multivariate Poisson Functionals
• On the Ornstein–Zernike equation for stationary cluster processes and the random connection model
• Stability of gas measures under perturbations and discretizations
• Lectures on the Poisson Process
• Statistical Mechanics of Lattice Systems
• On the construction of point processes in statistical mechanics
• An Introduction to the Theory of Point Processes
• Stochastic Analysis for Poisson Processes