A Course on Large Deviations with an Introduction to Gibbs Measures.

Contents
Preface (and to the reviewers) xi
Part I. Large Deviations: general theory and i.i.d. processes
Chapter 1. Introduction 3
§1.1. Information-theoretic entropy 5
§1.2. Thermodynamic entropy 6
Chapter 2. Preliminary examples and generalities 11
§2.1. Informal large deviations 11
§2.2. Formal large deviations 12
§2.3. Lower semicontinuity and uniqueness 15
Chapter 3. More generalities and Cramér’s theorem 19
§3.1. Weak large deviation principles 19
§3.2. Cramér’s theorem 21
§3.3. Limits, deviations, and fluctuations 27
Chapter 4. Yet some more generalities 29
§4.1. Contraction principle 29
§4.2. Varadhan’s theorem and Bryc’s theorem 31
§4.3. Curie-Weiss model for ferromagnetism 37
Chapter 5. Convex analysis in large deviation theory 41
§5.1. Some elementary convex analysis 41
§5.2. Rate function as a convex conjugate 49
vii