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＜E-Book＞
A course on large deviations with an introduction to Gibbs measures / Firas Rassoul-Agha, Timo Sepp�al�ainen
(Graduate Studies in Mathematics ; v. 162)

Publisher	(Providence, Rhode Island : American Mathematical Society)
Year	2015
Size	1 online resource (xiv, 318 pages)
Authors	*Rassoul-Agha, Firas Sepp�al�ainen, Timo O
Subjects	LCSH:Large deviations LCSH:Probabilities LCSH:Measure theory FREE:Probability theory and stochastic processes -- Instructional exposition (textbooks, tutorial papers, etc.)  All Subject Search FREE:Probability theory and stochastic processes -- Limit theorems -- Large deviations  All Subject Search FREE:Probability theory and stochastic processes -- Markov processes -- Markov chains (discrete-time Markov processes on discrete state spaces)  All Subject Search FREE:Probability theory and stochastic processes -- Special processes -- Interacting random processes; statistical mechanics type models; percolation theory  All Subject Search FREE:Probability theory and stochastic processes -- Special processes -- Processes in random environments  All Subject Search FREE:Statistical mechanics, structure of matter -- Equilibrium statistical mechanics -- Classical equilibrium statistical mechanics (general)  All Subject Search FREE:Statistical mechanics, structure of matter -- Equilibrium statistical mechanics -- Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs  All Subject Search
Contents	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 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 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 Appendix A. Analysis Appendix B. Probability Appendix C. Inequalities from statistical mechanics Appendix D. Nonnegative matrices
Notes	Includes bibliographical references (pages 299-303) and indexes Access is restricted to licensed institutions Electronic reproduction Providence, Rhode Island American Mathematical Society 2015 Mode of access : World Wide Web Description based on print version record HTTP:URL=http://www.ams.org/gsm/162 Information=Contents HTTP:URL=https://doi.org/10.1090/gsm/162 Information=Contents

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