Gibbs random fields: cluster expansions
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1991
|
| Series: | Mathematics and its applications / Soviet series
44 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | XIV, 248 S. |
| ISBN: | 079230232X |
Staff View
MARC
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| 100 | 1 | |a Malyšev, Vadim Aleksandrovič |e Verfasser |0 (DE-588)1104397889 |4 aut | |
| 240 | 1 | 0 | |a Gibbsovskie slučajnye polja |
| 245 | 1 | 0 | |a Gibbs random fields |b cluster expansions |c by V. A. Malyshev and R. A. Minlos |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1991 | |
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Record in the Search Index
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| adam_text | Contents
Preface xi
Notations xiii
Chapter 1. Gibbs Fields (Basic Notions) 1
§0 First Acquaintance with Gibbs Fields 1
§1 Gibbs Modifications 14
§2 Gibbs Modifications under Boundary Conditions and Definition
of Gibbs Fields by Means of Conditional Distributions 24
Chapter 2. Semi Invariants and Combinatorics 27
§1 Semi Invariants and Their Elementary Properties 27
§2 Hermite Ito Wick Polynomials. Diagrams. Integration by Parts 35
§3 Estimates on Moments and Semi In variants of Functionals
of Gaussian Families 43
§4 Connectedness and Summation over Trees 50
§5 Estimates on Intersection Number 59
§6 Lattices and Computations of Their Mobius Functions 63
viii Contents
§7 Estimate of Semi Invariants of Partially Dependent
Random Variables 68
§8 Abstract Diagrams (Algebraic Approach) 73
Chapter 3. General Scheme of Cluster Expansion 77
§1 Cluster Representation of Partition Functions and Ensembles
of Subsets 77
§2 Cluster Expansion of Correlation Functions 83
§3 Limit Correlation Function and Cluster Expansion of Measures 86
§4 Cluster Expansion and Asymptotics of Free Energy.
Analyticity of Correlation Functions 91
§5 Regions of Cluster Expansions for the Ising Model 95
§6 Point Ensembles 100
Chapter 4. Small Parameters in Interactions 104
§1 Gibbs Modifications of Independent Fields with
Bounded Potential 104
§2 Unbounded Interactions in the Finite Range Part of a Potential 108
§3 Gibbs Modifications of d Dependent Fields 110
§4 Gibbs Point Field in R 111
§5 Models with Continuous Time 115
§6 Expansion of Semi Invariants. Perturbation of a Gaussian Field 118
§7 Perturbation of a Gaussian Field with Slow Decay
of Correlations 122
Contents ix
§8 Modifications of d Markov Gaussian Fields (Interpolation
of Inverse Covariance) 127
Chapter 5. Expansions Around Ground States (Low Temperature
Expansions) 144
§1 Discrete Spin: Countable Number of Ground States 144
§2 Continuous Spin: Unique Ground State 149
§3 Continuous Spin: Two Ground States 155
Chapter 6. Decay of Correlations 163
§1 Hierarchy of the Properties of Decay of Correlations 163
§2 An Analytic Method of Estimation of Semi Invariants
of Bounded Quasi Local Functionals 167
§3 A Combinatorial Method of Estimation of Semi Invariants
in the Case of Exponentially Regular Cluster Expansion 172
§4 Slow (power) Decay of Correlations 180
§5 Low Temperature Region 187
§6 Scaling Limit of a Random Field 193
Chapter 7. Supplementary Topics and Applications 196
§1 Gibbs Quasistates 196
§2 Uniqueness of Gibbs Fields 204
§3 Compactness of Gibbs Modifications 210
§4 Gauge Field with Gauge Group Z? 214
§5 Markov Processes with Local Interaction 219
x Contents
§6 Ensemble of External Contours 226
Concluding Remarks 230
Bibliographic Comments 233
References 237
Subject Index 247
|
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| bvnumber | BV004611133 |
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| discipline | Mathematik |
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| id | DE-604.BV004611133 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:14:57Z |
| institution | BVB |
| isbn | 079230232X |
| language | English |
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| physical | XIV, 248 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Kluwer |
| record_format | marc |
| series2 | Mathematics and its applications / Soviet series |
| spelling | Malyšev, Vadim Aleksandrovič Verfasser (DE-588)1104397889 aut Gibbsovskie slučajnye polja Gibbs random fields cluster expansions by V. A. Malyshev and R. A. Minlos Dordrecht [u.a.] Kluwer 1991 XIV, 248 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 44 Aus d. Russ. übers. Zufälliges Feld (DE-588)4191094-1 gnd rswk-swf Gibbs-Maß (DE-588)4157328-6 gnd rswk-swf Cluster-Analyse (DE-588)4070044-6 gnd rswk-swf Zufälliges Feld (DE-588)4191094-1 s Cluster-Analyse (DE-588)4070044-6 s DE-604 Gibbs-Maß (DE-588)4157328-6 s Minlos, Robert A. Verfasser aut Soviet series Mathematics and its applications 44 (DE-604)BV004708148 44 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002832811&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Malyšev, Vadim Aleksandrovič Minlos, Robert A. Gibbs random fields cluster expansions Zufälliges Feld (DE-588)4191094-1 gnd Gibbs-Maß (DE-588)4157328-6 gnd Cluster-Analyse (DE-588)4070044-6 gnd |
| subject_GND | (DE-588)4191094-1 (DE-588)4157328-6 (DE-588)4070044-6 |
| title | Gibbs random fields cluster expansions |
| title_alt | Gibbsovskie slučajnye polja |
| title_auth | Gibbs random fields cluster expansions |
| title_exact_search | Gibbs random fields cluster expansions |
| title_full | Gibbs random fields cluster expansions by V. A. Malyshev and R. A. Minlos |
| title_fullStr | Gibbs random fields cluster expansions by V. A. Malyshev and R. A. Minlos |
| title_full_unstemmed | Gibbs random fields cluster expansions by V. A. Malyshev and R. A. Minlos |
| title_short | Gibbs random fields |
| title_sort | gibbs random fields cluster expansions |
| title_sub | cluster expansions |
| topic | Zufälliges Feld (DE-588)4191094-1 gnd Gibbs-Maß (DE-588)4157328-6 gnd Cluster-Analyse (DE-588)4070044-6 gnd |
| topic_facet | Zufälliges Feld Gibbs-Maß Cluster-Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002832811&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004708148 |
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