The Fourier Expansion and Basic Formulas
1:11:25Probability Densities and BLR Linearity Testing
1:12:46Social Choice and Influences
1:17:33Noise Stability and Arrow's Theorem
1:21:16Spectral Concentration and Learning
1:20:14Restrictions and the Goldreich-Levin Theorem
1:21:00DNF Formulas
1:15:56Linial-Mansour-Nisan Theorems
1:14:53Majority, LTFs, and the CLT
1:17:29LTFs and Noise Stability
1:18:29Level-1 Inequality and the 2/π Theorem
1:19:16Bonami's Lemma and the KKL Theorem
1:19:31Dictator Testing and the FKN Theorem
1:17:54Probabilistically Checkable Proofs of Proximity
1:16:10Constraint Satisfaction Problems
1:15:07Håstad's Hardness Theorems
1:18:41UG-Hardness Results from Dictator Tests
1:24:28The Hypercontractivity Theorem
1:17:32Invariance Theorems
1:17:58Majority Is Stablest Theorem
1:16:42Level-1 Inequality and the 2/π Theorem
This lecture introduces the Level-1 inequality and the precise 2/π Theorem, exploring their roles in characterizing the Fourier spectrum of Boolean functions, particularly for 'reasonable' random variables.
Analysis of Boolean Functions
Lecture 11: Level-1 inequality, 2/pi Theorem, Reasonable random variables
Carnegie Mellon graduate course 15-859S, Fall 2012