TY  - BOOK
AU  - Firas Rassoul-Agha 
AU  - Timo Seppäläinen 
TI  - A course on large deviations with an  to introduction to Gibbs measures
SN  - 9780821875780
AV  - QA 273.67 
PY  - 2015///]
CY  - Rhode Island
PB  - American Mathematical Society
KW  - Mathematics
N1  - 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 III. 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

N2  - This is an introductory course on the methods of computing asymptotics of probabilities of rare events: the theory of large deviations. The book combines large deviation theory with basic statistical mechanics, namely Gibbs measures with their variational characterization and the phase transition of the Ising model, in a text intended for a one semester or quarter course.

The book begins with a straightforward approach to the key ideas and results of large deviation theory in the context of independent identically distributed random variables. This includes Cramér's theorem, relative entropy, Sanov's theorem, process level large deviations, convex duality, and change of measure arguments. --- summary provided by publisher
ER  -