Chapter 20: Large Deviations and Concentration Inequalities

Learning Objectives

• State and prove Cramér's theorem, identifying the rate function as the Legendre-Fenchel transform of the log-MGF
• Explain Sanov's theorem and the role of KL divergence as the rate function for empirical distributions
• Define sub-Gaussian and sub-exponential random variables and derive their tail bounds
• Apply Hoeffding's inequality to sums of bounded random variables
• State the matrix Bernstein inequality and explain its relevance to massive MIMO analysis
• Connect large deviations to error exponents in hypothesis testing via Stein's lemma