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 19: Invariance Theorems (15-859)
This session covers invariance theorems, which elucidate how the structure of Boolean functions can be preserved under certain transformations, providing insights into their robustness and universality.
Analysis of Boolean Functions
Lecture 19: Invariance theorems
Carnegie Mellon graduate course 15-859S, Fall 2012
Lecture 18: The Hypercontractivity Theorem (15-859)
Next · Lecture 20Lecture 20: Majority Is Stablest Theorem (15-859)