Author | Ellis, Richard S. author |
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Title | Entropy, Large Deviations, and Statistical Mechanics [electronic resource] / by Richard S. Ellis |
Imprint | New York, NY : Springer New York, 1985 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-8533-2 |
Descript | XIV, 365 p. online resource |
I: Large Deviations and Statistical Mechanics -- I. Introduction to Large Deviations -- II. Large Deviation Property and Asymptotics of Integrals -- III. Large Deviations and the Discrete Ideal Gas -- IV. Ferromagnetic Models on ? -- V. Magnetic Models on ?D and on the Circle -- II: Convexity and Proofs of Large Deviation Theorems -- VI. Convex Functions and the Legendre-Fenchel Transform -- VII. Large Deviations for Random Vectors -- VIII. Level-2 Large Deviations for I.I.D. Random Vectors -- IX. Level-3 Large Deviations for I.I.D. Random Vectors -- Appendices -- Appendix A: Probability -- A.1. Introduction -- A.2. Measurability -- A.3. Product Spaces -- A.4. Probability Measures and Expectation -- A.S. Convergence of Random Vectors -- A.6. Conditional Expectation, Conditional Probability, and Regular Conditional Distribution -- A.7. The Kolmogorov Existence Theorem -- A.8. Weak Convergence of Probability Measures on a Metric Space -- Appendix B: Proofs of Two Theorems in Section II.7 -- B.1. Proof of Theorem II.7.1 -- B.2. Proof of Theorem II.7.2 -- Appendix C: Equivalent Notions of Infinite-Volume Measures for Spin Systems -- C.1. Introduction -- C.2. Two-Body Interactions and Infinite-Volume Gibbs States -- C.3. Many-Body Interactions and Infinite-Volume Gibbs States -- C.4. DLR States -- C.5. The Gibbs Variational Formula and Principle -- C.6. Solution of the Gibbs Variational Formula for Finite-Range Interactions on ? -- Appendix D: Existence of the Specific Gibbs Free Energy -- D.1. Existence Along Hypercubes -- D.2. An Extension -- List of Frequently Used Symbols -- References -- Author Index