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140122 ||| eng |
| 020 |
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|a 9789401137089
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| 100 |
1 |
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|a Malyshev, V.A.
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| 245 |
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|a Gibbs Random Fields
|h Elektronische Ressource
|b Cluster Expansions
|c by V.A. Malyshev, Robert A. Minlos
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| 250 |
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|a 1st ed. 1991
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| 260 |
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|a Dordrecht
|b Springer Netherlands
|c 1991, 1991
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| 300 |
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|a XIV, 248 p
|b online resource
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| 505 |
0 |
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|a 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 --
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| 505 |
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|a §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: UniqueGround State -- §3 Continuous Spin: Two Ground States -- 6. Decay of Correlations -- §1 Hierarchy of the Properties of Decay of Correlations --
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| 505 |
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|a §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
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| 653 |
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|a Complex Systems
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| 653 |
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|a Computer science / Mathematics
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| 653 |
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|a Discrete Mathematics in Computer Science
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| 653 |
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|a Probability Theory
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| 653 |
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|a System theory
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| 653 |
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|a Mathematical physics
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| 653 |
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|a Discrete mathematics
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| 653 |
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|a Theoretical, Mathematical and Computational Physics
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| 653 |
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|a Probabilities
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| 700 |
1 |
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|a Minlos, Robert A.
|e [author]
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Mathematics and its Applications, Soviet Series
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| 028 |
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|a 10.1007/978-94-011-3708-9
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| 856 |
4 |
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|u https://doi.org/10.1007/978-94-011-3708-9?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 519.2
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