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
1:16:42Majority, LTFs, and the CLT
This lecture explores the properties of Majority functions and Linear Threshold Functions (LTFs), linking them to the Central Limit Theorem (CLT) for approximating sums of random variables.
Analysis of Boolean Functions
Lecture 9: Majority, LTFs, and the CLT
Carnegie Mellon graduate course 15-859S, Fall 2012