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Recent Posts
 Call for nominations for the Ostrowski Prize 2017
 Problems for Imre Bárány’s Birthday!
 Twelves short videos about members of the Department of Mathematics and Statistics at the University of Victoria
 Jozsef Solymosi is Giving the 2017 Erdős Lectures in Discrete Mathematics and Theoretical Computer Science
 Updates (belated) Between New Haven, Jerusalem, and TelAviv
 Oded Goldreich Fest
 The Race to Quantum Technologies and Quantum Computers (Useful Links)
 Around the GarsiaStanley’s Partitioning Conjecture
 My Answer to TYI 28
Top Posts & Pages
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 Emmanuel Abbe: Erdal Arıkan's Polar Codes
 The Race to Quantum Technologies and Quantum Computers (Useful Links)
 Polymath 10 Emergency Post 5: The ErdosSzemeredi Sunflower Conjecture is Now Proven.
 From Oberwolfach: The Topological Tverberg Conjecture is False
 Problems for Imre Bárány's Birthday!
 R(5,5) ≤ 48
 Ziegler´s Lecture on the Associahedron
 Analysis of Boolean Functions
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Category Archives: Probability
Boolean Functions: Influence, Threshold, and Noise
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
Posted in Combinatorics, Computer Science and Optimization, Probability
Tagged Boolean functions
7 Comments
The US Elections and Nate Silver: Informtion Aggregation, Noise Sensitivity, HEX, and Quantum Elections.
Being again near general elections is an opportunity to look at some topics we talked about over the years. I am quite fond of (and a bit addicted to) Nate Silver’s site FiveThirtyEight. Silver’s models tell us what is the probability that … Continue reading
Posted in Combinatorics, Computer Science and Optimization, Probability, Quantum
Tagged Donald Trump, Hillary Clinton, Nate Silver
14 Comments
TYI 26: Attaining the Maximum
(Thanks, Dani!) Given a random sequence , ******, , let . and assume that . What is the probability that the maximum value of is attained only for a single value of ? Test your intuition: is this probability bounded … Continue reading
More Reasons for Small Influence
Readers of the bigleague ToC blogs have already heard about the breakthrough paper An averagecase depth hierarchy theorem for Boolean circuits by Benjamin Rossman, Rocco Servedio, and LiYang Tan. Here are blog reports on Computational complexity, on the Shtetl Optimized, and of Godel … Continue reading
Two Delightful Major Simplifications
Arguably mathematics is getting harder, although some people claim that also in the old times parts of it were hard and known only to a few experts before major simplifications had changed matters. Let me report here about two recent remarkable simplifications … Continue reading
Influence, Threshold, and Noise
My dear friend Itai Benjamini told me that he won’t be able to make it to my Tuesday talk on influence, threshold, and noise, and asked if I already have the slides. So it occurred to me that perhaps … Continue reading
Analysis of Boolean Functions week 5 and 6
Lecture 7 First passage percolation 1) Models of percolation. We talked about percolation introduced by Broadbent and Hammersley in 1957. The basic model is a model of random subgraphs of a grid in ndimensional space. (Other graphs were considered later as … Continue reading
Posted in Combinatorics, Computer Science and Optimization, Probability, Teaching
Tagged Arrow's theorem, Percolation
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Analysis of Boolean Functions – Week 3
Lecture 4 In the third week we moved directly to the course’s “punchline” – the use of FourierWalsh expansion of Boolean functions and the use of Hypercontractivity. Before that we started with a very nice discrete isoperimetric question on a … Continue reading
Analysis of Boolean functions – week 2
Post on week 1; home page of the course analysis of Boolean functions Lecture II: We discussed two important examples that were introduced by BenOr and Linial: Recursive majority and tribes. Recursive majority (RM): is a Boolean function with variables … Continue reading
Posted in Combinatorics, Computer Science and Optimization, Probability, Teaching
Tagged Boolean functions, Tribes
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Poznań: Random Structures and Algorithms 2013
Michal Karonski (left) who built Poland’s probabilistic combinatorics group at Poznań, and a sculpture honoring the Polish mathematicians who first broke the Enigma machine (right, with David Conlon, picture taken by Jacob Fox). Update: Here is a picture from 2015, while … Continue reading
Posted in Combinatorics, Conferences, Open problems, Philosophy, Probability
Tagged Poznan, RSA
2 Comments