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A Course on Large Deviations with an Introduction to Gibbs Measures
About this Title
Firas Rassoul-Agha, University of Utah, Salt Lake City, UT and Timo Seppäläinen, University of Wisconsin–Madison, Madison, WI
Publication: Graduate Studies in Mathematics
Publication Year:
2015; Volume 162
ISBNs: 978-0-8218-7578-0 (print); 978-1-4704-2222-6 (online)
DOI: https://doi.org/10.1090/gsm/162
MathSciNet review: MR3309619
MSC: Primary 60-01; Secondary 60F10, 60J10, 60K35, 60K37, 82B20
Table of Contents
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Front/Back Matter
Part I. Large deviations: General theory and i.i.d. processes
- Chapter 1. Introductory discussion
- Chapter 2. The large deviation principle
- Chapter 3. Large deviations and asymptotics of integrals
- Chapter 4. Convex analysis in large deviation theory
- Chapter 5. Relative entropy and large deviations for empirical measures
- Chapter 6. Process level large deviations for i.i.d. fields
Part II. Statistical mechanics
- Chapter 7. Formalism for classical lattice systems
- Chapter 8. Large deviations and equilibrium statistical mechanics
- Chapter 9. Phase transition in the Ising model
- Chapter 10. Percolation approach to phase transition
Part II. Additional large deviation topics
- Chapter 11. Further asymptotics for i.i.d. random variables
- Chapter 12. Large deviations through the limiting generating function
- Chapter 13. Large deviations for Markov chains
- Chapter 14. Convexity criterion for large deviations
- Chapter 15. Nonstationary independent variables
- Chapter 16. Random walk in a dynamical random environment
Appendixes
- Appendix A. Analysis
- Appendix B. Probability
- Appendix C. Inequalities from statistical mechanics
- Appendix D. Nonnegative matrices