Lecture 1: The Fourier Expansion and Basic Formulas (15-859)
1:11:25Lecture 2: Probability Densities and BLR Linearity Testing (15-859)
1:12:46Lecture 3: Social Choice and Influences (15-859)
1:17:33Lecture 4: Noise Stability and Arrow's Theorem (15-859)
1:21:16Lecture 5: Spectral Concentration and Learning (15-859)
1:20:14Lecture 6: Restrictions and the Goldreich-Levin Theorem (15-859)
1:21:00Lecture 7: DNF Formulas (15-859)
1:15:56Lecture 8: Linial-Mansour-Nisan Theorems (15-859)
1:14:53Lecture 9: Majority, LTFs, and the CLT (15-859)
1:17:29Lecture 10: LTFs and Noise Stability (15-859)
1:18:29Lecture 11: Level-1 Inequality and the 2/π Theorem (15-859)
1:19:16Lecture 12: Bonami's Lemma and the KKL Theorem (15-859)
1:19:31Lecture 13: Dictator Testing and the FKN Theorem (15-859)
1:17:54Lecture 14: Probabilistically Checkable Proofs of Proximity (15-859)
1:16:10Lecture 15: Constraint Satisfaction Problems (15-859)
1:15:07Lecture 16: Håstad's Hardness Theorems (15-859)
1:18:41Lecture 17: UG-Hardness Results from Dictator Tests (15-859)
1:24:28Lecture 18: The Hypercontractivity Theorem (15-859)
1:17:32Lecture 19: Invariance Theorems (15-859)
1:17:58Lecture 20: Majority Is Stablest Theorem (15-859)
1:16:42Lecture 20: Majority Is Stablest Theorem (15-859)
This final lecture presents the seminal "Majority Is Stablest" Theorem, demonstrating that the Majority function is maximally stable against noise, a key result in robust statistics and theoretical computer science.
Analysis of Boolean Functions
Lecture 20: Majority Is Stablest Theorem
Carnegie Mellon graduate course 15-859S, Fall 2012