Thermodynamic probability theory: some aspects of large deviations

Abstract

Contents 1. Introduction 279 2. The principle of the largest term 284 2.1. The general setting 284 2.2. The principle of the largest term 286 2.3. Upper and lower deviation functions 286 2.4. Concentration of measures on compact spaces 289 3. Vague large deviation principles and Ruelle-Lanford functions 291 3.1. Vague large deviation principles 291 3.2. Ruelle-Lanford functions 293 4. Examples 296 5. Narrow large deviation principles and exponential tightness 298 5.1. Narrow large deviation principles 298 5.2. Exponential tightness 300 5.3. Concentration of exponentially tight measures 303 6. Large deviation principles and Varadhan's theorems 304 6.1. Large deviation principles 304 6.2. Varadhan's theorems 304 7. Convexity 307 7.1. The scaled generating function 307 7.2. Weak law of large numbers and the differentiability of the pressure 311 Bibliography 316