- Proof By Lice!
- The seventeen camels riddle, and Noga Alon’s camel proof and algorithms
- Edmund Landau and the Early Days of the Hebrew University of Jerusalem
- Boolean Functions: Influence, Threshold, and Noise
- Laci Babai Visits Israel!
- Polymath10 conclusion
- Is Heads-Up Poker in P?
- The Median Game
- International mathematics graduate studies at the Hebrew University of Jerusalem
Top Posts & Pages
- The seventeen camels riddle, and Noga Alon's camel proof and algorithms
- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
- Proof By Lice!
- Updates and plans III.
- Amazing: Peter Keevash Constructed General Steiner Systems and Designs
- A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
- The Simplex, the Cyclic polytope, the Positroidron, the Amplituhedron, and Beyond
- Jim Geelen, Bert Gerards, and Geoﬀ Whittle Solved Rota's Conjecture on Matroids
- Polymath10-post 4: Back to the drawing board?
Category Archives: Probability
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
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
(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
Readers of the big-league ToC blogs have already heard about the breakthrough paper An average-case depth hierarchy theorem for Boolean circuits by Benjamin Rossman, Rocco Servedio, and Li-Yang Tan. Here are blog reports on Computational complexity, on the Shtetl Optimized, and of Godel … Continue reading
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
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
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 n-dimensional space. (Other graphs were considered later as … Continue reading
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
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
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