Tag Archives: Boolean functions

Boolean Functions: Influence, Threshold, and Noise

Posted on January 24, 2017 by Gil Kalai

Here is the written version of my address at the 7ECM last July in Berlin. Boolean functions, Influence, threshold, and Noise Trying to follow an example of a 1925 lecture by Landau (mentioned in the lecture), the writing style is very … Continue reading →

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Analysis of Boolean Functions – Week 3

Posted on September 18, 2013 by Gil Kalai

Lecture 4 In the third week we moved directly to the course’s “punchline” – the use of Fourier-Walsh expansion of Boolean functions and the use of Hypercontractivity. Before that we  started with  a very nice discrete isoperimetric question on a … Continue reading →

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Analysis of Boolean functions – week 2

Posted on September 8, 2013 by Gil Kalai

Post on week 1; home page of the course analysis of Boolean functions Lecture II: We discussed two important examples that were introduced by Ben-Or and Linial: Recursive majority and  tribes. Recursive majority (RM): is a Boolean function with variables … Continue reading →

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Analysis of Boolean Functions – week 1

Posted on September 3, 2013 by Gil Kalai

Home page of the course. In the first lecture I defined the discrete n-dimensional cube and  Boolean functions. Then I moved to discuss five problems in extremal combinatorics dealing with intersecting families of sets. 1) The largest possible intersecting family … Continue reading →

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Ryan O’Donnell: Analysis of Boolean Function

Posted on December 18, 2011 by Gil Kalai

Ryan O’Donnell has begun writing a book about Fourier analysis of Boolean functions and  he serializes it on a blog entiled Analysis of Boolean Function.  New sections appear on Mondays, Wednesdays, and Fridays. Besides covering the basic theory, Ryan intends to describe applications … Continue reading →

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Nati’s Influence

Posted on May 26, 2008 by Gil Kalai

When do we say that one event causes another? Causality is a topic of great interest in statistics, physics, philosophy, law, economics, and many other places. Now, if causality is not complicated enough, we can ask what is the influence one event has … Continue reading →

Posted in Combinatorics, Computer Science and Optimization, Open problems, Probability | Tagged , , , , , , , , , | 21 Comments