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Field name	Details
Dewey Class	519.2
Title	Gibbs Random Fields ([EBook]) : Cluster Expansions / by V. A. Malyshev, R. A. Minlos.
Author	Malyshev, V. A. (Vadim Aleksandrovich)
Added Personal Name	Minlos, R. A. (Robert Adolʹfovich)
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : Springer Netherlands , 1991.
Physical Details	XIV, 248 pages : online resource.
Series	Mathematics and its applications. Soviet series 0169-6378 ; ; 44
ISBN	9789401137089
Contents note	1. Gibbs Fields (Basic Notions) -- §0 First Acquaintance with Gibbs Fields -- §1 Gibbs Modifications -- §2 Gibbs Modifications under Boundary Conditions and Definition of Gibbs Fields by Means of Conditional Distributions -- 2. Semi-Invariants and Combinatorics -- §1 Semi-Invariants and Their Elementary Properties -- §2 Hermite-Itô-Wick Polynomials. Diagrams. Integration by Parts -- §3 Estimates on Moments and Semi-Invariants of Functional of Gaussian Families -- §4 Connectedness and Summation over Trees -- §5 Estimates on Intersection Number -- §6 Lattices and Computations of Their Möbius Functions -- §7 Estimate of Semi-Invariants of Partially Dependent Random Variables -- §8 Abstract Diagrams (Algebraic Approach) -- 3. General Scheme of Cluster Expansion -- §1 Cluster Representation of Partition Functions and Ensembles of Subsets -- §2 Cluster Expansion of Correlation Functions -- §3 Limit Correlation Function and Cluster Expansion of Measures -- §4 Cluster Expansion and Asymptotics of Free Energy. Analyticity of Correlation Functions -- §5 Regions of Cluster Expansions for the Ising Model -- §6 Point Ensembles -- 4. Small Parameters in Interactions -- §1 Gibbs Modifications of Independent Fields with Bounded Potential -- §2 Unbounded Interactions in the Finite-Range Part of a Potential -- §3 Gibbs Modifications of d-Dependent Fields -- §4 Gibbs Point Field in Rv -- §5 Models with Continuous Time -- §6 Expansion of Semi-Invariants. Perturbation of a Gaussian Field -- §7 Perturbation of a Gaussian Field with Slow Decay of Correlations -- §8 Modifications of d-Markov Gaussian Fields (Interpolation of Inverse Covariance) -- 5. Expansions Around Ground States (Low-Temperature Expansions) -- §1 Discrete Spin: Countable Number of Ground States -- §2 Continuous Spin: Unique Ground State -- §3 Continuous Spin: Two Ground States -- 6. Decay of Correlations -- §1 Hierarchy of the Properties of Decay of Correlations -- §2 An Analytic Method of Estimation of Semi-Invariants of Bounded Quasi-Local Functionals -- §3 A Combinatorial Method of Estimation of Semi-Invariants in the Case of Exponentially-Regular Cluster Expansion -- §4 Slow (power) Decay of Correlations -- §5 Low-Temperature Region -- §6 Scaling Limit of a Random Field -- 7. Supplementary Topics and Applications -- §1 Gibbs Quasistates -- §2 Uniqueness of Gibbs Fields -- §3 Compactness of Gibbs Modifications -- §4 Gauge Field with Gauge Group Z2 -- §5 Markov Processes with Local Interaction -- §6 Ensemble of External Contours -- Concluding Remarks -- Bibliographic Comments -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-94-011-3708-9
Links to Related Works	Subject References: Cluster analysis . Computer Science . Dynamical system . Probabilities . Probability theory and stochastic processes . Statistical Physics . Authors: author . Malyshev, V. A. (Vadim Aleksandrovich) . Minlos, R. A. (Robert Adolʹfovich) . See Also: Malyšev, Vadim A. . Corporate Authors: SpringerLink (Online service) . Series: Mathematics and its applications. Soviet series . Classification: 519.2 .

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Gibbs Random Fields: Cluster Expansions

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