Contents Abstract vii Chapter 1. Introduction 1 Chapter 2. History 5 Chapter 3. Overview 9 Chapter 4. Preliminaries 13 Chapter 5. Moments of the range 21 Chapter 6. Moderate deviations for Rn ERn 33 Chapter 7. Moderate deviations for ERn Rn 41 Chapter 8. Exponential asymptotics for the smoothed range 53 Chapter 9. Exponential approximation 65 Chapter 10. Laws of the iterated logarithm 73 Bibliography 81 v
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