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Interacting particle systems

Author: Thomas M Liggett
Publisher: New York u.a. : Springer, 1985.
Series: Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, 276
Edition/Format:   Print bookView all editions and formats
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Genre/Form: Wechselwirkendes Teilchensystem
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Thomas M Liggett
ISBN: 0387960694 9780387960692 3540960694 9783540960690
OCLC Number: 230825008
Description: XIII, 488 Seiten.
Contents: I The Construction, and Other General Results.- 1. Markov Processes and Their Semigroups.- 2. Semigroups and Their Generators.- 3. The Construction of Generators for Particle Systems.- 4. Applications of the Construction.- 5. The Martingale Problem.- 6. The Martingale Problem for Particle Systems.- 7. Examples.- 8. Notes and References.- 9. Open Problems.- II Some Basic Tools.- 1. Coupling.- 2. Monotonicity and Positive Correlations.- 3. Duality.- 4. Relative Entropy.- 5. Reversibility.- 6. Recurrence and Transience of Reversible Markov Chains.- 7. Superpositions of Commuting Markov Chains.- 8. Perturbations of Random Walks.- 9. Notes and References.- III Spin Systems.- 1. Couplings for Spin Systems.- 2. Attractive Spin Systems.- 3. Attractive Nearest-Neighbor Spin Systems on Z1.- 4. Duality for Spin Systems.- 5. Applications of Duality.- 6. Additive Spin Systems and the Graphical Representation.- 7. Notes and References.- 8. Open Problems.- IV Stochastic Ising Models.- 1. Gibbs States.- 2. Reversibility of Stochastic Ising Models.- 3. Phase Transition.- 4. L2 Theory.- 5. Characterization of Invariant Measures.- 6. Notes and References.- 7. Open Problems.- V The Voter Model.- 1. Ergodic Theorems.- 2. Properties of the Invariant Measures.- 3. Clustering in One Dimension.- 4. The Finite System.- 5. Notes and References.- VI The Contact Process.- 1. The Critical Value.- 2. Convergence Theorems.- 3. Rates of Convergence.- 4. Higher Dimensions.- 5. Notes and References.- 6. Open Problems.- VII Nearest-Particle Systems.- 1. Reversible Finite Systems.- 2. General Finite Systems.- 3. Construction of Infinite Systems.- 4. Reversible Infinite Systems.- 5. General Infinite Systems.- 6. Notes and References.- 7. Open Problems.- VIII The Exclusion Process.- 1. Ergodic Theorems for Symmetric Systems.- 2. Coupling and Invariant Measures for General Systems.- 3. Ergodic Theorems for Translation Invariant Systems.- 4. The Tagged Particle Process.
Series Title: Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, 276
Responsibility: Thomas M. Liggett.

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